Question

On the first day a total of 40 items were sold for $356. Define the variables and write a system of equations to find the number of cakes and pies sold

Answer 1

Question:

On the first day, a total of 40 items were sold for $356. Pies cost $10 and cakes cost $8. Define the variables, write a system of equations to find the number of cakes and pies sold, and state how many pies were sold.

Answer:

The variables are defined as:

"c" represent the number of cakes sold and "p" represent the number of pies sold

The system of equations used are:

c + p = 40 and 8c + 10p = 356

18 pies and 22 cakes were sold

Solution:

Let "c" represent the number of cakes sold

Let "p" represent the number of pies sold

Cost of 1 pie = $ 10

Cost of 1 cake = $ 8

Given that total of 40 items were sold

number of cakes + number of pies = 40

c + p = 40 ------ eqn 1

Given items were sold for $356

number of cakes sold x Cost of 1 cake + number of pies sold x Cost of 1 cake = 356

$c \times 8 + p \times 10 = 356$

8c + 10p = 356  ----- eqn 2

Let us solve eqn 1 and eqn 2

From eqn 1,

p = 40 - c    ---- eqn 3

Substitute eqn 3 in eqn 2

8c + 10(40 - c) = 356

8c + 400 - 10c = 356

-2c = - 44

c = 22

Substitute c = 22 in eqn 3

p = 40 - c

p = 40 - 22

p = 18

Thus 18 pies and 22 cakes were sold