Question

Maya bought a dozen specialty donuts at the bakery for $18. She purchased a mixture of frosted donuts for $2 each, glazed donuts for $1 each, and custard filled donuts for $5 each. If Maya purchased twice as many frosted donuts as custard filled donuts, how many of each type of donut did she buy? Variables: mixture of frosted donuts X y = glazed donuts Z = custard filled donuts System: System in standard form:​

Answer 1

The quantity of frosted donuts = 2

The quantity of glazed donuts = 9

The quantity of custard filled donuts = 1

Explanation:

Let the quantity of frosted donuts =
`x`

Let the quantity of glazed donuts =
`y`

Let the quantity of custard filled donuts =
`z`

As per question statements, following equations can be made:

`x+y+z=12......(1)\\2x+y+5z=18.....(2)\\x=2z ...... (3)`

Putting
`x=2x` in (1) and (2):

`y+3z=12 .... (4)\\y+9z=18 .... (5)`

Subtracting (4) from (5):

`6z=6\\\Rightarrow z =\bold{1}`

By equation (3):

`x=\bold{2}`

By equation (1):

`y=\bold{9}`

Therefore, the answers are:

The quantity of frosted donuts = 2

The quantity of glazed donuts = 9

The quantity of custard filled donuts = 1