Question

Bilquis is preparing many gifts for a family holiday party. Each gift must

either be wrapped with wrapping paper or prepared in a gift bag. Bilquis car
wrap a single gift in 4.5 minutes and she can do a giftbag in 2 minutes.
Bilquis prepared a total 21 gifts in 79.5 minutes. Write a system of equations
that could be used to determine the number of gifts Bilquis wrapped and the
number of giftbags she prepared. Define the variables that you use to write
the system.

Answer 1

• w + b = 21
• 4.5w +2b = 79.5

Explanation:

You want a system of equations to represent the scenario that Bilquis prepared 21 gifts in 79.5 minutes when wrapping took 4.5 minutes and bagging took 2 minutes.

Setup

Let w represent the number of wrapped gifts, and b represent the number of bagged gifts. We can write the equations ...

• w + b = 21 . . . . . . . . . . . . . total number of gifts prepared
• 4.5w +2b = 79.5 . . . . . . . . total preparation time

Solution

This problem statement does not ask for a solution, but it is not difficult to obtain one. Substitute for b and solve for w:

b = 21 -w

4.5w +2(21 -w) = 79.5

2.5w +42 = 79.5

2.5w = 37.5

w = 37.5/2.5 = 15

b = 21 -15 = 6

Bilquis wrapped 15 gifts and bagged 6 of them.