Question

50 points

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:

A

y=10 x 2.5 +25

y= 25+25

y=50

y=10 x 5 +25

y=50+25

y=75

y=10 x 15 +25

y=150+25

y=175

y=10 x 75 +25

y=750+25

y=775

B

y= 5 x 2.5 + 50

y=12.5 + 50

y=62.5

y = 5 x 5 + 50

y=25+50

y=75

y = 5 x 15 + 50

y=75+50

y=125

y = 5 x 75 + 50

y= 375 +50

y=425

So its 5 weeks since both get 25

You can also do a equation method

5x + 50=10x + 25

-5x( )-5x

50=5x+25

-25( )-25

25=5x

÷5( )÷5

5=x

so 5 weeks again