Question

Six pears and three apples cost $3.90. Two pears and five apples cost $3.30. How much does one pear cost?

Answer 1

Let's first translate that in "the language".

Explanation:

`6*p+3*a=3.90and2*p+5*a=3.30`
We multiply the second equation (all of it) by 3, because that will also give us the price of 6 pears plus apples (as in the first), and the price difference will only be caused by the different number of apples:

`6*p+15*a=9.90` now subtract the other equation:
`-(6*p+3*a=3.90)`
So: `12*a=6.00->a=0.50` (=price of an apple)

Put this into one of the equations:
`2*p+5*0.50=3.30->2*p=3.30-2.50=0.80->`
`p=0.40` (price of a pear)

Check!
`6*0.40+3*0.50=3.90and2*0.40+5*0.50=3.30`