Question

A bakery sells doughnuts for $1.00, muffins for $1.50 bagles for $1.20. The bakery makes three times as many doughnuts as bagels. If the bakery sells all 130 items in stock, they earn a total of $150. How many items are in stock at the bakery? Justify your answer. [Hint: use D for the # of doughnuts, M for the # of muffins and B for the # of bagels.]

Answer 1

As given in the question

use D for the number of doughnuts,

M for the number of muffins and B for the number of bagels.

The bakery makes three times as many doughnuts as bagels

equations becomes

D = 3B

bakery sells all 130 items in stock

equations becomes

D + B + M = 130

Bakery earn a total of $150

equations becomes

1.00D + 1.50M+ 1.20B = 150

On simplier terms

1D + 1.5M + 1.2B = 150

three equation are become in the form

D = 3B

D + B + M = 130

1D + 1.5M + 1.2B = 150

subract D + B + M = 130 equation from 1D + 1.5M + 1.2B = 150

1D -1D + 1.5M -M + 1.2B -1B = 150 -130

0.5M + 0.2B = 20

in simple form

5M + 2B = 200

Put D = 3B in the equation D + B + M = 130

we get

4B + M = 130

Now multiply 4B + M = 130 by 5 and subtracted from 5M + 2B = 200

5M - 5M + 2B - 20 B = 200 - 650

-18 B = - 450

B = 25

Put this value in the D = 3B

we get

D = 25× 3

= 75

Put the value of D and B in the equation D + B + M = 130 .

75 + 25 + M= 130

130 - 100 = M

M = 30

items are in stock at the bakery is doughnuts = 75 , muffins = 30 , bagels = 25.

Hence proved