Question

Sarah and George wanted to buy some sweets so they decided to buy brownies and banana bread Sarah bought four boxes of brownies and six loaves of banana bread George bought five boxes of brownies and three loaves of banana bread is Sarah spent $44 and George spent $37 determine how much the cost is for a box of brownies and a loaf of banana bread

Answer 1

Cost of a box of brownies = $5

Cost of a loaf of banana bread = $4

Explanation:

Let, x= box of brownies.

y=loaf of banana bread.

Now,

Sarah bought 4 boxes of brownies and 6 loaves of banana at $44, after expressing this in equation form we get:-

`4x+6y=44` --------------------------(equation 1)

And George bought 5 boxes of brownies and 3 loaves of banana at $37, after expressing this in equation form we get:-

`5x+3y=37` --------------------------(equation 2)

Now,

`4x+6y=44`

`4x=44-6y`

`x=(44-6y)/(4)`

`x=11-(6)/(4)y`

`x=11-(3)/(2)y`------------------(equation 3)

Now substituting equation 3 in equation 2 we get,

`5x+3y=37`

`5(11-(3)/(2)y)+3y=37`

`55-((15)/(2)* y) +3y=37`

`55-37=((15)/(2)* y)-3y`

`18=7.5y-3y`

`18=4.5y`

`y=4` ----------------------------------(Equation 4)

Now putting value of y from equation 4 in equation 3

i.e.
`x=11-(3)/(2)y`

`x=11-(3* 4)/(2)`

`x=11-6`

`x=5`

Therefore the cost of a box of brownies = $5

the cost of a loaf of banana bread = $4