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MANUFACTURING A shoe manufacturer spends $2.50 to make sandals and $4 to make running shoes. During a typical month, they spend $2500 manufacturing sandals and running shoes. During the month of April, they double the pairs of sandals manufactured and spend a total of $3000.




How many pairs of sandals and running shoes does the company make during a typical month?

Sagot :

MrRoyal

Answer:

200 pairs of sandals

Step-by-step explanation:

Represent the sandals with x and the running shoes with y.

In a typical month:

[tex]Total = 2500[/tex]

In April

[tex]Total = 3000[/tex]

Required

The number of sandals in a typical month

In a typical month:

If 1 sandal costs 2.50, then x costs 2.50x

If 1 running shoe costs 4, then y costs 4y

The total is:

[tex]2.50x + 4y = 2500[/tex]

In April:

If 1 sandal costs 2.50, then 2x costs 5x ---- we used 2x because the pairs is doubled

If 1 running shoe costs 4, then y costs 4y

The total is:

[tex]5x + 4y = 3000[/tex]

The equations are:

[tex]5x + 4y = 3000[/tex]

[tex]2.50x + 4y = 2500[/tex]

Subtract

[tex]5x - 2.50x + 4y - 4y = 3000 - 2500[/tex]

[tex]2.50x = 500[/tex]

[tex]x = \frac{500}{2.50}[/tex]

[tex]x = 200[/tex]

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