At a bake shop, the cost of flour is $2.50 per pound and increases at a rate of $0.07 per month. The cost of cocoa is $6.00 per pound and decreases at a rate of $0.03 per month. If the trends continue, which system of equations can be used to find the number of months, x, when the price, y, is equal for both flour and cocoa?

Step-by-step explanation:

We will find two equations for this system, one representing flour and the other representing cocoa. For the flour, we start with $2.50, and the cost goes up. 07 per month, x. The equation for that is

y =.07x + 2.50

For the cocoa, the equation is written in the exact same way, but the cost goes down. Down is a negative thing while up is a positive thing. The cost starts at $6.00 and goes down. 03 per month, x. The equation for that is

y = -.03x + 6.00

Comparing the first equation to the second, the. 07 is positive because the cost goes UP that amount per month and the. 03 is negative because the cost goes DOWN that amount per month. Get it?

If y is cost and we are tryong to find out where the cost is the same, we are looking for when y is the same. If the first y is equal to. 07x + 2.50 and the second y is equal to -.03x + 6.00, and y is equal to y, then

.07x + 2.50 = -.03x + 6.00 (this is setting the first y equal to the second y). This is the system that describes how to find the number of months x when the cost y is the same. We'll solve it just for practice.

Combining like terms we get

.10x = 3.5 so

x = 35

Now back sub in what x equals to solve for y. If x = 35, then in the first equation,

.07 (35) + 2.50 = y and

y = 4.95 (you could have used the second equation and subbed in 35 for x and you will get the exact same y value. Promise!)

What this answer tells us is that 35 months after the start of this pricing, the cost of flour will be the same as the cost of cocoa. But immediately after 35 months, the costs will not be the same anymore. It is only AT 35 months. At 36 months, the costs will be different.