Question

At a hockey game, a vender sold a combined total of 235 sodas and hot dogs. The number of hot dogs sold was 59 less than the number of sodas sold. Find the number of sodas sold and the number of hot dogs sold.

Answer 1

• 147 sodas
• 88 hot dogs

Explanation:

This problem is similar to many others in which the sum of two quantities and their difference are given. The solution can be found easily when the equations for the relations are written in standard form.

Setup

Let s and h represent numbers of sodas and hot dogs sold, respectively. The given relations are ...

• s +h = 235 . . . . . combined total
• s -h = 59 . . . . . . difference in the quantities

Solution

Adding the two equations eliminates one variable.

(s +h) +(s -h) = (235) +(59)

2s = 294 . . . . simplify

s = 147 . . . . . .divide by 2

h = 147 -59 = 88 . . . . h is 59 less

147 sodas and 88 hot dogs were sold.

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Additional comment

The solution to a "sum and difference" problem is always the same. One of the numbers is half the sum of those given, and the other is half their difference. ((235-59)/2 = 88)