Hannah H. answered • 06/19/20
Previous University Finance Tutor
So, the best thing to do here is to create two equations. The reason why is because the apples and grapes share a relationship, so what's true for one equation has to be true for the other, and having constraints like that makes it easier to solve anyways.
Apples cost 1.25 per pound and grapes cost 2.60 per pound. It says they spent a total of 35.80. So, these constraints give us our first equation.
1.25A + 2.60G = 35.80
It also says that they ordered a total of 20 pounds. So, this constraint gives us our second equation. They bought pounds of both apples and grapes, but they bought exactly 20 pounds, no more, no less. So, we get this for the second equation.
A + G = 20
So, now the amount of apples and grapes we bought must add up to 20 pounds and we know it must also add up to $35.80. This ensures there's only one answer, and we don't have to guess or do any trial and error.
So now lets put them together.
1.25A + 2.60G = 35.80
A + G = 20
We have two variables. In order to solve, we need to manipulate at least one of the equations so that when we combine them, it will cancel out one of the variables, leaving only one variable to solve for. And then once you have one variable it is easy to solve for the other. So how can I change the equations so that either A or G disappears? If I multiply the 2nd equation by (-1.25), you will have 1.25A and -1.25A. These will cancel out when we "add" the equations together.
(A + G = 20) X (-1.25) =
-1.25A - 1.25G = -25
So now lets put them together!
-1.25A - 1.25G = -25
+ 1.25A + 2.60G = 35.80
1.35G = 10.80
G = 10.80 / 1.35 = 8
So, they bought 8 pounds of grapes. Since we know they bought a total of 20 pounds, you can easily find that they bought 12 pounds of apples.
