Question

The number of new slides must be more than three times the number of new swing sets. Each swing set costs $275 and each slide costs $168. They can spend no more than $1,250.

Answer 1

Explanation:

sl = number of slides

sw = number of swing sets

sl > 3×sw

since we are dealing with integers here (there cannot be parts of slides or swing sets), this means

sl >= 4×sw

sl×168 + sw×275 <= 1250

(4×sw)×168 + sw×275 <= 1250

672×sw + 275×sw <= 1250

947×sw <= 1250

sw <= 1250/947

sw <= 1.319957761...

again, we are dealing with integers here, so, we need to round to the lower integer, and therefore, they can afford to buy only 1 swing set.

that leaves $1250 - $275 = $975 for slides.

how many ?

975 / 168 = 5.803571429...

again, we are only handling whole slides, and have to round down to the lower integer.

therefore, they can afford to buy 5 slides (which satisfies the criteria of "more than 3 times the number of swing sets").

so, they buy

1 swing set $275

5 slides $840 (5×$168)

-------------------------

$1,115

that leaves them with $1250 - $1115 = $135.