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?

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Answer 1 · 2016-07-26T16:39:13

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.

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)

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
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 $3m-3m=0$

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

$" "c=5.35-3m...........................(2_a)$
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Substitute $(2_a)$ into (1)

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

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

$" "16.05-7m=10.8$

$" "7m=16.05-10.8$

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

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

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

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