Tammy makes $ 7 per hour plus $4 for each item she sells, and lisa makes $10 per hour plus 3.00 for each item she sells. in an hour, how many items do they need to sell to make the same amount of money?

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Answer: 3

Tammy and Lisa will make the same amount of money when they each sell 3 items. It'll probably never happen, though, since Tammy is a much better saleswoman than Lisa. You should hear her in action: "What will it take to put you in this foot spa today?" What a pro.

Now let's do the same problem in symbols. We need to find the two equations described by the problem.

Tammy's line has a y-intercept of 7 and a slope of 4, so her equation is

y = 4x + 7.

Lisa's line has a y-intercept of 10 and a slope of 3, so her equation is

y = 3x + 10.

We've found a system of equations:

The problem asks how many items sold will give Tammy and Lisa the same amount of money, so we want to find x when the y-values on the two lines are the same. That is, we want to find where the lines intersect, which we can do by solving the system of equations. Why did one line cross the other line? To get to the other side. Oh ... you've probably heard the version with the chicken.

For this system, it's easiest to use substitution. Since y = 4x + 7, we have

We think if each girl sells 3 items, they'll be paid the same. Let's check this: if Tammy sells 3 items, she makes 7 + 3 (4) = 19 dollars.

And if Lisa sells 3 items she makes 10 + 3 (3) = 19 dollars. It's a match.