Question

In a certain candy store, 3 pounds of candy and 2 pounds of mints cost $10.80, and 1 pound of candy and 3 pounds of mints cost $5.35. What is the cost per pound of the mints?

Answer 1

Mints cost `$3/4` per pound
I have taken you up to this point and given a strong hint about to solve the next bit.

Explanation:

The trick with these question to 'get rid of 1 of the unknowns so that you can solve for the remaining one.

Let the cost of candy per pound be `c`
Let the cost of mints per pound be `m`

Then we have:

`3c+2m=$10.80`.............................(1)
`c+3m=$5.35`....................................(2)

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Consider equation(2)

`" "color(brown)(c+3m=5.35)`

Subtract `color(blue)(3m)` from both sides

`" "color(brown)(c+3mcolor(blue)(-3m)=5.35color(blue)(-3m))`

But `3m-3m=0`

`" "c+0=5.35-3m`

`" "c=5.35-3m...........................(2_a)`
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Substitute `(2_a)` into (1)

`color(brown)(3c+2m=$10.80)color(blue)(" "->" "3(5.35-3m)+2m=10.8`

`" "16.05-9m+2m=10.8`

`" "16.05-7m=10.8`

`" "7m=16.05-10.8`

`" "7m=5.25 larr" note that 5.25 is " 5 1/4`

`" " m= 1/(cancel(7)^1)xx(cancel(21)^3)/4 =`

`" "m=3/4`
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`color(green)("I will let you solve for the cost of candy")`

Hint: substitute `m=3/4` in one of the original equations