Answer:
- Flowers: $19.98
- Jewelry: $18.92
- Gift Certificates: $14.52
Explanation:
You want the values of three expenditures, given three relations between them.
(The first thing to realize is that the question isn't about averages at all. It is about values that are described as averages.)
Setup
Let f, j, c represent the (average) amounts spent on flowers, jewelry, and gift certificates, respectively. The three given relations are ...
f + j + c = 53.42
j = 4.40 + c
f + c = 15.58 + j
Solution
Using the second equation to substitute for j in the third, we have ...
f +c = 15.58 +(4.40 +c)
f = 19.98 . . . . . . . . . . . . . . simplify
Using this and the second equation to substitute into the first, we have ...
19.98 +(4.40 +c) +c = 53.42
24.38 +2c = 53.42
2c = 29.04
c = 14.52
Then ...
j = 4.40 +c = 4.40 +14.52 = 18.92
The average expenditures are ...
- Flowers: $19.98
- Jewelry: $18.92
- Gift Certificates: $14.52
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Additional comment
This solution is one of many ad hoc methods that could be used. There are also graphing and matrix methods available for solving a set of equations like this. The attachment shows a calculator matrix solution.