Question

Wade and Ida are salespeople who earned the same amount this week, although Ida made 4 more sales than Wade. Wade earns a base of $153 plus $22 per sale. Ida earns a base of $17 plus $24 per sale. Write the equation for the number of sales Wade made this week

Answer 1

y = 24x + 17 20

Explanation:

Firstly, let's say that 153 and 17 are both the y-intercepts of their respective equations, while 22 and 24 are the slope. With this we can create the following set of equations:

y = 24x + 17

y = 22x + 153

So your answer would be y = 24x + 17

Now let's find the sales answer!

Since we know that Ida made 4 more sales than Wade this week, we could say:

y = 24(x+4) + 17

y = 22x + 153

Now since we know that they earned the same amount we can do the following:

24(x+4) + 17 = 22x + 153

Simplify...

24x + 96 + 17 = 22x + 153

Simplify again:

24x + 113 = 22x + 153

subtract 22x and 113 from both sides...

2x = 40

Then:

x = 20

So this means that Wade made 20 sales this week!

So let's check if we are right:

Now that we know that x = 20, we need to plug it into Wade's equation!

y = 22(20) + 153

y = 440 + 153

y = 593

Wade made $593 this week!

To check if we are right, let's plug it into Ida's equation:

y = 24x + 113

y = 24(20) + 113

y = 480 +113

y = 593

Ida also made $593 this week!

MEANING we are right!

I hope I helped :P