This handy Spectrum Math Grade 7 Answer Key Chapter 5 Lesson 5.2 Problem Solving provides detailed answers for the workbook questions
Spectrum Math Grade 7 Chapter 5 Lesson 5.2 Problem Solving Answers Key
A scale drawing is a drawing of a real object in which all of the dimensions are proportional to the real object. A scale drawing can be larger or smaller than the object it represents. The scale is the ratio of the drawing size to the actual size of the object.
A drawing of a person has a scale of 2 inches = 1 foot. If the drawing is 11 inches high, how tall is the person?
Write a proportion.
\(\frac{2}{1}\) = \(\frac{11}{n}\) Solve for n.
\(\frac{1\times 11}{2}\) = n Solve for n.
5\(\frac{1}{2}\) = n The person is 5\(\frac{1}{2}\) feet tall.
Solve each problem. Write a proportion in the space to the right.
Question 1.
A bridge is 440 yards long. A scale drawing has a ratio of 1 inch = 1 yard. How long is the drawing?
The drawing is ______________ inches long.
Answer:
The drawing is 440 inches long.
Explanation:
Given that,
A scale drawing has a ratio of 1 inch = 1 yard.
440 yards = 440 inch.
Question 2.
A map of the county uses a scale of 2 inches = 19 miles. If the county is 76 miles wide, how wide is the map?
The map is _____________ inches wide.
Answer:
The map is 8 inches wide.
Explanation:
Given that,
A scale of 2 inches = 19 miles.
The county is 76 miles
Write a proportion.
\(\frac{2}{19}\) = \(\frac{n}{76}\) Solve for n.
\(\frac{2\times 76}{19}\) = n
n = 2 x 4 = 8 inches.
Question 3.
A picture of a goldfish has a scale of 8 centimeters to 3 centimeters. If the actual goldfish is 12 centimeters long, how long is the drawing?
The drawing is _____________ centimeters long.
Answer:
The drawing is 32 centimeters long.
Explanation:
Given that,
a scale of 8 centimeters to 3 centimeters.
the actual goldfish is 12 centimeters long,
a scale of 8 cm = 3 cm.
goldfish is 12 centimeters long, Write a proportion.
\(\frac{8}{3}\) = \(\frac{n}{12}\) Solve for n.
\(\frac{8\times 12}{3}\) = n
n = 8 x 4 = 32 cm.
Question 4.
An architect made a scale drawing of a house to be built. The scale is 2 inches to 3 feet. The house in the drawing is 24 inches tall. How tall is the actual house?
The actual house is _______________ feet tall.
Answer:
The actual house is 36 feet tall.
Explanation:
Given that,
a scale of 2 inch to 3 ft.
a scale of 2 in. = 3 ft.
house in the drawing is 24 inches tall.
Write a proportion.
\(\frac{2}{3}\) = \(\frac{24}{n}\) Solve for n.
\(\frac{3\times 24}{2}\) = n
n = 3 x 12 = 36 ft.
Solve each problem. Write a proportion in the space to the right.
Question 1.
On an architect’s blueprint, the front of a building measures 27 inches. The scale of the blueprint is 1 inch = 2 feet. How wide will the front of the actual building be?
The building will be _______________ feet wide.
Answer:
The building will be 54 feet wide.
Explanation:
Given that,
The scale of the blueprint is 1 inch = 2 feet.
the front of a building measures 27 inches.
Write a proportion.
\(\frac{1}{2}\) = \(\frac{27}{n}\) Solve for n.
\(\frac{2\times 27}{1}\) = n
n = 2 x 27= 54 ft.
Question 2.
The model of an airplane has a wingspan of 20 inches. The model has a scale of 1 inch = 4 feet. What is the wingspan of the actual airplane?
The wingspan is _______________ feet.
Answer:
The wingspan is 80 feet.
Explanation:
Given that,
The model has a scale of 1 inch = 4 feet.
The model of an airplane has a wingspan of 20 inches.
Write a proportion.
\(\frac{1}{4}\) = \(\frac{20}{n}\) Solve for n.
\(\frac{4\times 20}{1}\) = n
n = 4 x 20= 80 ft.
Question 3.
A picture of a car uses a scale of 1 inch = \(\frac{1}{2}\) foot. The actual car is 8\(\frac{1}{2}\) feet wide. How wide will the drawing of the car be?
The drawing will be ______________ inches wide.
Answer:
The drawing will be 17 inches wide.
Explanation:
Given that,
The actual car is 8\(\frac{1}{2}\) feet wide.
A picture of a car uses a scale of 1 inch = \(\frac{1}{2}\) foot.
Write a proportion.
\(\frac{1}{0.5}\) = \(\frac{n}{8.5}\) Solve for n.
\(\frac{1\times 8.5}{0.5}\) = n
n = 8.5 / 0.5= 17 ft.
Question 4.
On a map, two cities are 4\(\frac{1}{4}\) if inches apart. The scale of the map is \(\frac{1}{2}\) inch = 3 miles. What is the actual distance between the towns?
The actual distance is _____________ miles.
Answer:
The actual distance is 25\(\frac{1}{2}\) miles.
Explanation:
Given that,
two cities on map are 4\(\frac{1}{4}\) inches apart.
The scale of the map is \(\frac{1}{2}\) inch = 3 miles.
Write a proportion.
\(\frac{0.5}{3}\) = \(\frac{4.25}{n}\) Solve for n.
\(\frac{3\times 4.25}{0.5}\) = n
n = 12.75 / 0.5= 25.5 miles.
25\(\frac{1}{2}\) miles
Question 5.
Marisa is making a scale drawing of her house. Her house is 49 feet wide. On her drawing, the house is 7 inches wide. What is the scale of Marisa’s drawing?
The scale is ________________.
Answer:
The scale is 1 inch = 7 feet.
Explanation:
Given that,
On Marisa drawing, the house is 7 inches wide, house is 49 feet wide.
The scale is 7 inch = 49 feet.
The scale is 1 inch = 49/7 = 7 feet.
Question 6.
The bed of Jeff’s pick-up truck is 8 feet long. On a scale model of his truck, the bed is 10 inches long. What is the scale of the model?
The scale is _______________.
Answer:
The scale is 1 inch = \(\frac{4}{5}\) foot.
Explanation:
Given that,
The bed of Jeff’s pick-up truck is 8 feet long.
On a scale model of his truck, the bed is 10 inches long.
The scale is 10 inch = \(\frac{8}{10}\) foot.
The scale is 1 inch = \(\frac{4}{5}\) foot.