Question

Malik stops at the grocery store to buy a bag of diapers and 2 cans of formula. He spends a total of $37. The next week he stops and buys 2 bags of diapers and 5 cans of formula for a total of $87. How much does a bag of diapers cost? How much is one can of formula?

Answer 1

Cost of a bag of diapers is $11 and cost of one can of formula is $13.

Explanation:

Let cost of each diaper = $D and cost of each cans of formula = $C

Malik shops a bag of diapers and 2 cans of formula.

He spends total of $37.

So the equation will be

D + 2C = 37 -------(1)

Next week he stops and buys 2 bags of diapers and 5 cans of formula.

He spends total $87.

Equation for this purchase will be

2D + 5C = 87 ----------(2)

Multiply equation (1) by 2 and subtract it from equation (2).

2(D + 2C) - (2D + 5C) = 2×37 - 87

2D + 4C - 2D - 5C = 74 - 87

-C = - 13

C = 13

From equation (1)

D + 2×13 = 37

D + 26 = 37

D = 37 - 26

D = 11

Therefore, cost of a bag of diapers is $11 and cost of one can of formula is $13.

Answer 2

Diapers costs $11 and formula is $13.

Explanation:

Let's name diapers as A and formula as B.

Simply the equations:

1A + 2B = $37(1)

2A + 5B = $87(2)

Clear D from one equation.

A = $37 - 2B(1)

Replace D into the other equation.

2*($37 - 2B) + 5B = $87(2)

$74 - 4B + 5B = $87

$74 + B = $87

B = $87 - $74 = $13

Find A, now knowing B.

A = $37 - 2($13)

A = $37 - $26 = $11