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

Answer:

The quantity of frosted donuts = 2

The quantity of glazed donuts = 9

The quantity of custard filled donuts = 1

Step-by-step 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