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Two glasses of milk and 3 snack bars have a total of 61 carbohydrates​ (carbs), and 4 glasses of milk and 2 snack bars have a total of 70 carbs. Determine how many carbs are in one glass of milk and in one snack bar.

Respuesta :

MrRoyal

Answer:

24 carbohydrates

Step-by-step explanation:

Represent Snack bars with S and Milks with M.

So, we have:

[tex]2M\ and\ 3S\ = 61[/tex]

and

[tex]4M\ and\ 2S\ = 70[/tex]

Required: Solve for M and S

Convert the given expressions to mathematical expressions:

[tex]2M + 3S = 61[/tex] --- (1)

[tex]4M + 2S = 70[/tex] --- (2)

Multiply the first equation by 2

[tex]2M + 3S = 61[/tex] --------- * 2

[tex]4M + 6S = 122[/tex] --- (3)

Subtract (1) from (3)

[tex]4M - 4M + 6S - 2S = 122 - 70[/tex]

[tex]4S = 52[/tex]

Solve for S

[tex]S = 52/4[/tex]

[tex]S = 13[/tex]

Substitute 13 for S in (2)

[tex]4M + 2S = 70[/tex]

[tex]4M + 2 * 13 = 70[/tex]

[tex]4M + 26 = 70[/tex]

Solve for 4M

[tex]4M = 70 - 26[/tex]

[tex]4M = 44[/tex]

Solve for M

[tex]M = 44/4[/tex]

[tex]M = 11[/tex]

1 glass of milk and 1 snack bar = S + M

[tex]S + M = 13 + 11[/tex]

[tex]S + M = 24[/tex]

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