We included HMH Into Math Grade 7 Answer Key PDF Module 7 Lesson 3 Write Two-Step Equations for Situations to make students experts in learning maths.
HMH Into Math Grade 7 Module 7 Lesson 3 Answer Key Write Two-Step Equations for Situations
I Can write two-step equations for various situations.
Spark Your Learning
Write an equation to represent each scenario.
Scenario 1: The cook at Sam’s Diner made 19 quiches today. This is 1 more than 3 times the number of quiches he made yesterday. How many quiches did he make yesterday?
Answer:
6
Explanation:
He made 6 quiches yesterday.
Scenario 2: Javier buys four dozen eggs. He saves $1.50 by using a coupon. The total he pays is $8.50. What was the cost of a dozen eggs without the coupon?
Answer:
$2.50
Explanation:
The cost of a dozen eggs without a coupon is $2.50.
Scenario 3: Lina ate \(\frac{1}{4}\) of a quiche for lunch. Each of her two sisters split another piece equally. The three ate a total of \(\frac{7}{12}\) of the quiche. What fraction of the quiche did each of Lina’s sisters eat?
Answer:
Turn and Talk Choose one of the equations you wrote. Make up another scenario that the equation could represent.
Answer:
Build Understanding
Question 1.
The perimeter of an isosceles triangle is 60 feet. The base is 12 feet long. Write an equation that could be used to find the lengths of the congruent sides.
Answer:
Given,
The sides of the isosceles triangle are a = x ft, b = 12 ft
The perimeter of the isosceles triangle is 2 (a + b)
Given perimeter is 60 feet.
60 feet = 2 (a +b)
60 = 2 ( x + 12)
\(\frac{60}{2}\) = (x + 12)
30 = x + 12
x = 30 -12
x = 18 feet.
A. Write an expression for the perimeter (in feet) of the isosceles triangle. Use the variable x to stand for the unknown information.
+ +
Answer:
a + a + b
60 = 2 ( x + 12)
B. Combine any like terms in the expression.
+
Answer:
C. What is the value of the expression you wrote?
Answer:
x = 18 feet.
D. Use your answers from Parts B and C to write an equation that can be used to find the length of each of the two equal sides.
Answer:
E. How would your equation change if the perimeter were 80 feet?
Answer:
80 = 2 (x + 10).
F. What would your equation be if the perimeter were 80 feet and the base were 10 feet long?
Answer:
The equation is 80 = 2 (x + 10).
Given
Perimeter = 80 feet and base = 10 feet.
Let us assume one side of the traingle is x
a = x feet
p = 2(a + b)
80 = 2 (x + 10)
Turn and Talk How is an equation like an expression? How is it different?
Answer:
Step It Out
Question 2.
Chelsea buys a shirt and shoes at the store with the coupon at the right. The price of the shirt before the discount is $22, and her total discount is $18.55. Write an equation to find the price of the shoes before the discount.
A. What information are you trying to find? How can a variable help determine that information?
Answer:
We need to find the price of the shoes before the discount.
B. Write an equation that can be used to find the unknown information. Use x as the variable.
Answer:
0.5(22 + x) = 18.55
C. What does each side of the equation represent?
Answer:
Each side of the equation represents before the discount and after the discount given.
D. What does the variable x represent?
Answer:
X represents the price of the shoes before the discount.
Check Understanding
Question 1.
Each time Cheryl runs, she runs 3 miles. She rides her bike only on Saturdays and always for 10 miles. She exercises the same amount each week. She rides and runs for a total of 22 miles in a week. Write an equation that can be used to find out how many times Cheryl goes running each week.
Answer:
3x + 10y = 22
Explanation:
An equation that can be used to find out how many times Cheryl goes running each week is 3x + 10y = 22.
Question 2.
Mrs. Wu uses a 25% off coupon to buy 1 adult ticket and 1 child ticket to a movie. She pays a total amount of $9.00. A child ticket without the coupon costs $4.00. Write an equation that can be used to find the cost of an adult ticket without the coupon.
Answer:
cost of an adult ticket is $7.25.
Explanation:
An equation that can be used to find the cost of an adult ticket without the coupon is
11.25 – 4 = $7.25
On Your Own
Model with Mathematics For Problems 3-8, write an equation to represent the situation.
Question 3.
Carl is making the kite shown. It has a perimeter of 120 inches. The two longer sides of the kite are the same length. Write an equation that could be used to find the length of each of the longer sides.
Answer:
2x + 48 = 120
Explanation:
Given,
Perimeter us 120inches
Sides are 24 inches + 24 inches = 48 inches
Two longer sides + (24 × 2) = 120 inches
(2 × x) + 48 = 120
2x = 120 – 48
2x = 72
x = 72 ÷ 2
x = 36
Question 4.
Ms. Malia bought a laptop with a 10% discount. She also bought a mouse for $13.99 and spent a total of $621.49 before taxes. Write an equation to find the original cost of the laptop.
Answer:
$675
Explanation:
The original cost of the laptop is x
Given discount = 10%
Price of mouse = $13.99
Total amount spent is $621.49
x – x \(\frac{10}{100}\) + 13.99 = 621.49
x – \(\frac{x}{10}\) + 13.99 = 621.99
\(\frac{9x}{10}\) + 13.99 = 621.99
\(\frac{9x}{10}\) = 621.99 -13.99
\(\frac{9x}{10}\) = 607.5
9x = 607.5 × 10
x = 6075 ÷ 9
x = $675
Question 5.
Paolo is using his grandmother’s cookie recipe. He always doubles the amount of chocolate chips and oats. The recipe calls for 2\(\frac{1}{2}\) cups of chocolate chips. The total amount of chips and oats after doubling is 6\(\frac{1}{3}\) cups. Write an equation to find the original amount of oats in the recipe.
Answer:
x = 1 \(\frac{11}{12}\)
Explanation:
Given,
The total amount of chips and oats is 6\(\frac{1}{3}\)
Recipe calls for 2\(\frac{1}{2}\)
6\(\frac{1}{3}\) – 2\(\frac{1}{2}\) = 2x
\(\frac{19}{3}\) – \(\frac{5}{2}\) = 2x
\(\frac{23}{6}\) = 2x
\(\frac{23}{12}\) = x
x = 1\(\frac{11}{12}\)
Question 6.
A square has side lengths as shown in the picture and a perimeter of 54.8 centimeters. Write an equation to find the value of x.
Answer:
Equation to find length = 4 (x + 3) = 54.8
x = 10.7 cm
Explanation:
Length = x + 3
Perimeter of the square = 4 × length = 54.8
4 (x + 3) = 54.8
x + 3 = 54.8 ÷ 4
x + 3 = 13.7
x = 13.7 – 3
x = 10.7
Each side of the length = 10.7
Question 7.
Ms. Emily buys a hat and gloves with a coupon for 30% off her entire purchase. The gloves cost $35 before the discount. Her biH before tax is $44.80. Write an equation to find the original cost of the hat.
Answer:
($35 + x) (1 – 0.3) 44.80
Question 8.
Bo’s sister Anna is \(\frac{3}{4}\) his age minus 1 year. She is 11 years old. Write an equation to find Bo’s age.
Answer:
Bo’s age is 16.
Explanation:
Let us solve the given question based on the given conditions.
\(\frac{3}{4}\) × x – 1 = 11
Now solve the given equation
\(\frac{3}{4}\)x = 11 + 1
\(\frac{3}{4}\)x = 12
x = 12 × \(\frac{4}{3}\)
x = 16.
Bo’s age is 16.
I’m in a Learning Mindset!
What barriers do I perceive to writing two-step equations for situations?
Answer:
Lesson 7.3 More Practice/Homework
Question 1.
Pierce is making a rectangular frame for a photo collage that has a perimeter of 72.2 inches. The length of the frame is 20.3 inches. Write an equation to find the width of the frame.
Answer:
x = \(\frac{79}{5}\).
Explanation:
From the given question,
2(20.3 + x) = 72.2
Let us solve the equation
Now expand the given expression
40.6 + 2x = 72.2
2x = 72.2 – 40.6
2x = 31.6
x = 31.6 ÷ 2
x = 79 ÷ 5
Question 2.
Kendra is 3 times her daughter’s age plus 7 years. Kendra is 49 years old. Write an equation to find her daughter’s age.
Answer:
Her daughter’s age is 14.
Explanation:
Let us solve the given question
7 + 3x = 49
3x = 49 – 7
3x = 42
Divide both sides
x = 42 ÷ 3
simplify
x = 14
Question 3.
Mitchell orders a plain turkey sandwich and a drink for lunch. The drink is $2.95. Instead he is served the super sandwich with lettuce, tomato, and mayonnaise. The restaurant manager takes 15% off the price of the sandwich. Write an equation to determine the original price of Mitchell’s sandwich if his new bill is $8.05.
Answer:
Original price is $6
Explanation:
The original price of the sandwich is $x.
The drink is $2.95
$2.95 + (1 – 0.15) x = $8.05
$2.95 + 0.85 x = $8.05
0.85x = $8.05 -$2.95
0.85x = $5.1
x = $5.1 ÷ 0.85
x = $6
Question 4.
Bianca and Meredith are sisters. Meredith’s height is \(\frac{2}{3}\) of Bianca’s height plus 32 inches. Meredith is 60 inches tall. Write an equation to find Bianca’s height in inches.
Answer:
Bianca’s height is 42 inches.
Explanation:
Let us assume Bianca’s height as x.
\(\frac{2}{3}\) × x + 32 = 60
\(\frac{2}{3}\) × x = 60 – 32
\(\frac{2}{3}\) × x = 28
x = (28 × 3) ÷ 2
x = 84 ÷ 2
x = 42
Therefore Bianca’s height is 42 inches.
Question 5.
Health and Fitness Tyler does squats and pushups. He wants to increase the number of each type of exercise by 20% by the end of the month. He currently does 25 pushups. If Tyler meets his goal, he will do a total of 13 more squats and pushups than he does now. Write an equation to find how many squats Tyler does now.
Answer:
x = 40
Explanation:
Let us solve the given question
25 × 20% + x × 20% = 13
5 + 0.2x = 13
0.2x = 13 – 5
0.2x = 8
x = 8 ÷ 0.2
x = 80 ÷ 2
x = 40
Therefore Tyler does 40 squats.
Question 6.
Model with Mathematics An equilateral triangle has side lengths that measure x + 4 inches. The perimeter of the triangle is 18.6 inches. Write an equation to find the value of x.
Answer:
x = 2.2
Explanation:
Given is an equilateral triangle
Side is x + 4 inches
Perimeter is 18.6 inches.
The three sides of an equilateral traingle are equal
x + 4 = 18.6 ÷ 3
x + 4 = 6.2
x = 6.2 – 4
x = 2.2
Question 7.
Model with Mathematics Ms. Lynette earns $19.50 an hour when she works overtime. She worked overtime twice this week. One day she worked 3 hours of overtime. Her total overtime pay for the week is $146.25. Write an equation to find the number of overtime hours worked on the second day.
Answer:
4.5 hours
Explanation:
Let us assume the the number of overtime hours worked on the second day as x
3 × 19.5 + 19.5 × x = 146.25
58.5 + 19.5x = 146.25
19.5x = 146.25 -58.5
19.5x = 87.75
x = 87.75 ÷ 19.5
x = 4.5 hours
Test Prep
Question 8.
A parallelogram has a perimeter of 50\(\frac{1}{2}\) inches. The two longer sides of the parallelogram are each 16\(\frac{1}{4}\) inches. Write an equation to find the length of each of the shorter sides.
Answer:
Question 9.
A baby usually gains 10% of its birth weight plus 2 pounds in the first six weeks after birth. A baby gained 2.8 pounds. Write an equation to find the baby’s birth weight.
Answer:
1.1x + 2 = 2.8
Explanation:
Gain 10% = 100% + 10%
= 110%
= 1.1
Let us assume the baby’s birth weight as x.
Now let us solve the given question
1.1x + 2 = 2.8
Question 10.
A rhombus has sides of length x + 6 inches and a perimeter of 49 inches. Which equation represents this situation?
(A) 4x + 6 = 49
(B) 4(x + 6) – 49
(C) x + 6 = 49
(D) x + 24 = 49
Answer:
(B) 4(x + 6) – 49
Explanation:
Rhombus has four equal sides
Perimeter = 4 × side
length = x + 6
Perimeter = 49 inches
Side = x + 6
4 (x + 6) = 49
Question 11.
Mrs. Owens has a coupon for 40% off a pair of shoes. She pays $111.79 for a pair of shoes and a dress after using the coupon. The dress costs $64.99. Which equation can be solved for x, the retail price of the shoes?
(A) 0.6x + 64.99 = 111.79
(B) 0.4x + 64.99 = 111.79
(C) 0.6(x + 64.99) = 111.79
(D) 0.4(x + 64.99) = 111.79
Answer:
(A) 0.6x + 64.99 = 111.79
Explanation:
From the given question
Calculate the given question
(64.99 + 40% of x) × (1 – 40%) = 111.79
0.6x + 64.99 = 111.79
Spiral Review
Question 12.
Sarah began the school week with $2.60 in her lunch account. She deposited $20 on Monday, and then spent $4.75 each day that week for lunch. What was the balance in her lunch account at the end of the day on Friday?
Answer:
-1.15
Explanation:
Based on the given question calculate
2.6 + 20 – 4.75 × 5
2.6 + 20 – 23.75
22.6 – 23.75
-1.15
The balance in her lunch account at the end of the day on Friday is -1.15.
Question 13.
Mr. Alvarado goes shopping at the mall with $70. He buys a pair of pants for $33.76 and a shirt for $29.52. He also returns a hat he bought the previous week for $19.67. How much money does Mr. Alvarado have after he buys the pants and shirt and returns the hat?
Answer:
$26.39
Explanation:
Mr. Alvarado went for shopping with $70.
Pair of pants for $33.76
The hat he brought = $19.67
The money Mr. Alvarado have is 70 – 29.52 – 33.76 + 19.67 = 26.39