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Estelle is helping at a community food drive by boxing up cans of soup. There are two sizes of boxes, large and small. Estelle fills 3 large boxes and 5 small boxes with 170 soup cans total. The boy working next to her fills 4 large boxes and 4 small boxes with 184 soup cans total. How many cans does each small box hold?

Respuesta :

MrRoyal

Answer:

The small box contains 21 cans

Step-by-step explanation:

Represent the small box with S and the large with L.

For Estelle:

[tex]3L + 5S = 170[/tex]

For the boy:

[tex]4L + 4S = 184[/tex]

Required

Determine the cans in the small box

[tex]3L + 5S = 170[/tex] --- (1)

[tex]4L + 4S = 184[/tex] --- (2)

Divide (2) through by 4

[tex]L + S = 46[/tex]

Make L the subject

[tex]L = 46 -S[/tex]

Substitute 46 - S for L in (1)

[tex]3L + 5S = 170[/tex]

[tex]3(46 - S) + 5S = 170[/tex]

Open bracket

[tex]128 - 3S + 5S = 170[/tex]

[tex]128 + 2S = 170[/tex]

Collect Like Terms

[tex]2S = 170-128[/tex]

[tex]2S = 42[/tex]

Divide both sides by 2

[tex]S = 21[/tex]

Hence, the small box contains 21 cans

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