## Engage NY Eureka Math 7th Grade Module 4 Mid Module Assessment Answer Key

### Eureka Math Grade 7 Module 4 Mid Module Assessment Task Answer Key

Question 1.

In New York, state sales tax rates vary by county. In Allegany County, the sales tax rate is 8 1/2%.

a. A book costs $12.99, and a video game costs $39.99. Rounded to the nearest cent, how much more is the tax on the video game than the tax on the book?

Answer:

12.99(8.5%) = 12.99(0.085) = 1.10415

39.99(8.5%) = 39.99(0.085) = 3.39915

3.39915 – 1.10415 = 2.295

= $ 2.30

b. Using n to represent the cost of an item in dollars before tax and t to represent the amount of sales tax in dollars for that item, write an equation to show the relationship between n and t.

Answer:

t = 0.085 n

c. Using your equation, create a table that includes five possible pairs of solutions to the equation. Label each column appropriately.

Answer:

d. Graph the relationship from parts (b) and (c) in the coordinate plane. Include a title and appropriate scales and labels for both axes.

Answer:

e. Is the relationship proportional? Why or why not? If so, what is the constant of proportionality? Explain.

Answer:

Yes, the relationship is proportional because the graph of the equation is a straight line that touches the origin. Also, the table shows that the ratio of the \(\frac{\text { amount of sales tax }}{\text { cost of an item }}\) equal 0.085.

\(\frac{0.085}{1}=\frac{0.17}{2}=\frac{0.255}{3}=\frac{0.34}{4}=\frac{0.425}{5}\)

The constant of proportionality is 0.085 because that is the sales tax amount for $ 1.00, which is the unit rate.

f. In nearby Wyoming County, the sales tax rate is 8%. If you were to create an equation, graph, and table for this tax rate (similar to parts (b), (c), and (d)), what would the points (0,0) and (1,0.08) represent? Explain their meaning in the context of this situation.

Answer:

The point of origin (0, 0) means that no tax has been applied yet because nothing has been purchased. The point (1, 0.08) is the unit rate, or the constant of proportionality. It means that for an item that costs $ 1.00, the amount of tax applied is $ 0.08. The unit rate also shows that for every 1.00, the amount of tax will increase by $ 0.08.

g. A customer returns an item to a toy store in Wyoming County. The toy store has another location in Allegany County, and the customer shops at both locations. The customer’s receipt shows $2.12 tax was charged on a $24.99 item. Was the item purchased at the Wyoming County store or the Allegany County store? Explain and justify your answer by showing your math work.

Answer:

The item was purchased in allegany county

\(\frac{2.12}{24.99}\) is about, \(\frac{2.12}{25} \times 4\) = \(\frac{8.48}{100}\),

Which is 8.48%, or about 8.5%.

Question 2.

Amy is baking her famous pies to sell at the Town Fall Festival. She uses 32\(\frac{1}{2}\) cups of flour for every 10 cups of sugar in order to make a dozen pies. Answer the following questions below and show your work.

a. Write an equation, in terms of f, representing the relationship between the number of cups of flour used and the number of cups of sugar used to make the pies.

Answer:

f = \(\frac{13}{4}\) S

b. Write the constant of proportionality as a percent. Explain what it means in the context of this situation.

Answer:

3.25 = \(\frac{325}{100}\) = 3.25%

A constant of proportionality of 325% means that the amount of flour used to make the pies is 325% the amount of sugar used.

c. To help sell more pies at the festival, Amy set the price for one pie at 40% less than what it would cost at her bakery. At the festival, she posts a sign that reads, “Amy’s Famous Pies—Only $9.00/Pie!” Using this information, what is the price of one pie at the bakery?

Answer:

The price of one pie at the bakery is $15.00.