Question

The cost of two coffees and four icecreams is 22 cents. The cost of three coffees and five icecreams is 30 cents. Value of a coffe is? Value of an icecream is?

Answer 1

let x be coffess and y be ice cream
so 2x+4 =22
3x+5y=30
now solve these simulataneously

Answer 2

Yes, but it isn't quite that easy. You try.

Answer 3

c = coffee
i = ice cream

2c + 4i = .22 ---> (3)2c + 4i = .22
3c + 5i = .30 --->(-2)3c + 5i = .30
--------------
6c + 12i = .66 (result of multiplying by 3)
-6c - 10i = - .60 (result of multiplying by -2)
--------------add
0 + 2i = .06
......i = .06/2
......i = .03

now sub .03 in for i in either of the original equations
2c + 4i = .22
2c + 4(.03) = .22
2c + .12 = .22
2c = .22 - .12
2c = .10
c = .10/2
c = .05

check by subbing in known values into either of the original equations
3c + 5i = .30 2c + 4i = .22
3(.05) + 5(.03) = .30 2(.05) + 4(.03) = .22
.15 + .15 = .30 .10 + .12 = .22
.30 = .30 (correct) .22 = .22 (correct)

Coffee costs 5 cents and ice cream costs 3 cents

Do you understand what I just did ? Do you have any questions ?

Answer 4

I do have a question. Why do we multiply by a negative 2?

Answer 5

This is an elimination problem. That means you have to eliminate a variable in order to find the value of the other variable. I chose to eliminate the c variable. In order to do that, I had to make the c's opposite of each other. One has to be a negative 6 and one has to be a positive 6. If one is negative and one is positive, of course having the same coefficient, then they will cancel each other out. -6 and + 6 cancel(eliminate) each other. Thus, letting us solve for i.
Does that make sense ?

Answer 6

Thank you so much!

Answer 7

your welcome :) Glad to help