Question

A store sells toys in bulk. It sells wooden blocks for $5 a pound and plastic bricks for $10

a pound. How many pounds of wooden blocks and plastic bricks should be used to make a
10-pound mixture that would sell for $80?

Answer 1

4 pounds of wooden blocks and 6 pounds of plastic bricks should be used.

Explanation:

Let w = wooden block

Let p = plastic bricks

Given the following data;

Price of wooden block per pounds = $5

Price of plastic brick per pounds = $10

*Translating the word problem into an algebraic equation*

For the 10-pound mixture;

`w + p = 10` .........equation 1

For the $80 mixture;

`5w + 10p = 80` ..........equation 2

Solving the linear equation by using the substitution method;

Making w the subject in equation 1:

`w = 10 - p` .......equation 3

Substituting "w" into equation 2;

`5(10 - p) + 10p = 80`

Simplifying the equation, we have;

`50 - 5p + 10p = 80`

`50 + 5p = 80`

Rearranging the equation, we have;

`5p = 80 - 50`

`5p = 30`

`p = \frac {30}{5}`

p = 6 pounds (For the plastic brick).

To find w;

Substituting "p" into equation 3;

`w = 10 - 6`

w = 4 pounds (For the wooden block).