Question

The cost of 3 subs and 7 cookies is $18.75. Five subs and 21 cookies cost

Answer 1

One sub costs $4.5 and one cookie costs $0.75 or 75 cents

Step-by-step explanation:

Let s be the cost of one sub

and

c be the cost of one cookie

Then according to given statements

"The cost of 3 subs and 7 cookies is $18.75"

$3s+7c = 18.75\ \ \ Eqn\ 1$

"Five subs and 21 cookies cost  $38.25"

$5s+21c = 38.25\ \ \ \ Eqn\ 2$

Multiplying eqn 1 by 3

$9s+21c = 56.25\ \ \ Eqn\ 3$

Subtracting Eqn 2 from Eqn 3

$9s+21c- (5s+21c) = 56.25-38.25\\9s+21c-5s-21c = 18\\4s = 18$

Dividing both sides by 4

$\frac{4s}{4} =\frac{18}{4}\\s = 4.5$

Putting s=4.5 in Eqn 1

$3s+7c = 18.75\\3(4.5)+7c = 18.75\\13.5+7c = 18.75\\7c = 18.75-13.5\\7c =5.25$

Dividing both sides by 7

$\frac{7c}{7}=\frac{5.25}{7}\\c = 0.75$

So,

One sub costs $4.5 and one cookie costs $0.75 or 75 cents

Keywords: Linear Equations, Variables

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