SOLUTION: plan international offers gifts of hope options where you select a gift to support a community in a developing country. it costs 500 euros to equip a school room and 295 euros to s

Question 1181298: plan international offers gifts of hope options where you select a gift to support a community in a developing country. it costs 500 euros to equip a school room and 295 euros to send a girl to school. If you buy 20 gifts at a total cost of 6515 euros, how many classrooms will be equipped and how many girls will be sent to school.
Answer by greenestamps(13198) (Show Source): You can put this solution on YOUR website!

A total of 20 gifts that cost either 295 or 500 euros each are being bought, and a total of 6515 euros is being spent. You need to determine how many of each are being bought.

For a student just learning basic algebra, I see three basic ways to set up this problem for solving.

(1) Using two equations and elimination

let x = # of gifts at 295 euros each
let y = # of gifts at 500 euros each

x+y=20
295x+500y=6515

With two equations in this form, usually solving by elimination is easiest.

(2) Using two equations and substitution.

You can start the same way as in (1), but instead of using elimination, solve the first equation to get y=20-x and substitute that into the second equation.

(3) Using a single equation

let x = # of gifts at 295 euros each
then 20-x = # of gifts at 500 euros each

Then you only need to solve a single equation to find the answer:

295(x)+500(20-x)=6515

I personally would never use method (2) above, because it is exactly like method (3) but with an extra step. For me, methods (1) and (3) are equally good.

Try the different methods and find one that "works" best for you.

And here is my personal favorite for a fast way to solve this kind of problem, if a formal algebraic solution is not required.

20 gifts all at 295 euros each would cost 5900 euros; the actual total is 6515 euros, which is another 615 euros.
The difference in the cost between the two gifts is 500-295=205 euros.
To make the needed additional 615 euros, the number of higher priced gifts must be 615/205=3.

ANSWER: 3 gifts at 500 euros each; 17 at 295 euros each.

CHECK: 500(3)+295(17) = 1500+5015 = 6515

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