Question

1 Thomas uses a graphing calculator to solve the following word problem. Two shirts and five pairs of pants cost $150. Three shirts and four pairs of pants cost $190. Find the cost of a shirt. Select the statements that describe the steps that Thomas can use to solve the problem using his graphing c A Let x equal the cost of a shirt and y equal the cost of a pair of pants. B Solve each equation for y. c Solve each equation for r. D The solution is the point where the lines intersect. E The solutions are the points where the lines intersect the y-axis.​

Answer 1

The correct options are;

A. Let x equal the cost of a shirt and y equal the cost of a pair pants

B. Solve each equation for y

D. The solution is the point where the lines intersect

Explanation:

The cost of two shirts and five pants = $150

Three shirts and four pairs of pants = $190

Let x = The cost of a shirt and y = the cost of a pair of pants

We have;

2·x + 5·y = 150

3·x + 4·y = 190

We solve each equation for y, to get;

For the first equation, we have;

2·x + 5·y = 150

5·y = 150 - 2·x

y = 150/5 - 2/5·x = 30 - 2/5·x

y = 30 - 2/5·x

For the second equation, we have;

3·x + 4·y = 190

4·y = 190 - 3·x

y = 190/4 - 3/4·x = 47.5 - 3/4·x

y = 47.5 - 3/4·x

The solution is the point where the two lines intersect, which is given as follows;

y = y

47.5 - 3/4·x = 30 - 2/5·x

17.5 = 3/4·x - 2/5·x = 7/20·x

x = 20/7 × 17.5 = 50

The cost of a shirt = x = $50

The cost of a pair of pant = y = 30 - 2/5·x = 30 - 2/5 × 50 = 10

The cost of a pair of pant = $10.