Question

The administrative assistant at a software company often provides breakfast when there is a morning meeting. For last week's sales meeting, she purchased 7 dozen doughnuts and 3 dozen croissants, spending a total of $53. In preparation for yesterday's safety meeting, she spent $35 on 1 dozen doughnuts and 5 dozen croissants. Assuming she purchased the items at the same bakery both times, how much does a dozen of each cost?

Answer 1

A dozen of doughnuts cost $5 and a dozen of croissants cost $6.

Step-by-step explanation:

Let,

Cost of 1 dozen doughnuts = x

Cost of 1 dozen croissants = y

According to given statement;

7x+3y = 53     Eqn 1

x+5y = 35      Eqn 2

Multiplying Eqn 2 by 7

$77(x+5y = 35)\\x+35y=245\ \ \ Eqn\ 3$

Subtracting Eqn 1 from Eqn 3

$(7x+35y)-(7x+3y)=245-53\\7x+35y-7x-3y=192\\32y=192$

Dividing both sides by 32

$\frac{32y}{32}=\frac{192}{32}\\y=6$

Putting y=6 in Eqn 2

$x+5(6)=35\\x+30=35\\x=35-30\\x=5$

A dozen of doughnuts cost $5 and a dozen of croissants cost $6.

Keywords: linear equation, elimination method

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