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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?

Respuesta :

Lanuel

Answer:

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

Step-by-step 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;

[tex] w + p = 10[/tex] .........equation 1

For the $80 mixture;

[tex] 5w + 10p = 80[/tex] ..........equation 2

Solving the linear equation by using the substitution method;

Making w the subject in equation 1:

[tex] w = 10 - p[/tex] .......equation 3

Substituting "w" into equation 2;

[tex] 5(10 - p) + 10p = 80 [/tex]

Simplifying the equation, we have;

[tex] 50 - 5p + 10p = 80 [/tex]

[tex] 50 + 5p = 80 [/tex]

Rearranging the equation, we have;

[tex] 5p = 80 - 50[/tex]

[tex] 5p = 30 [/tex]

[tex] p = \frac {30}{5} [/tex]

p = 6 pounds (For the plastic brick).

To find w;

Substituting "p" into equation 3;

[tex] w = 10 - 6[/tex]

w = 4 pounds (For the wooden block).

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