Question

Question 7(Multiple Choice Worth 2 points)

(Systems of Linear Equations MC)

Two siblings, sibling A and sibling B, are saving money for their summer vacation. The amount of money that sibling A has in their savings account, y, can be represented by the equation y = 10x + 25, where x represents the number of weeks. Sibling B's savings can be represented by the equation y = 5x + 50.

Based on the graph of this system of linear equations, after how many weeks will their savings accounts have the same amount of money?

2.5 weeks
5 weeks
15 weeks
75 weeks

Answer 1

5 weeks

Explanation:

the two linear equations are:

sibling (A) and sibling (B)

y = 10x + 25 and y = 5x + 50

where y = mx + c

and x represents the number of weeks

after how many weeks will their savings accounts have the same amount of money i.e. for which value of x will both equations have the same value

inserting the value of x in both equations:

for x = 2.5 A = 50 and B = 62.5

for x = 5 A = 75 and B = 75

for x = 15 A = 175 and B = 125

for x = 75 A = 775 and B = 425

thus, after 5 weeks both siblings A and B will have the same amount of money in their accounts

Answer 2

the answer is B, 5 weeks.