Question

Beth and Pranav are selling cheesecakes for a school fundraiser. Customers can buy New York

Answer 1

Answer:

Cost of one New York style cheesecake  = $5

Cost of one apple cheesecake = $9

Step-by-step explanation:

Let cost of one New York style cheesecake be = $x$

Let cost of one apple cheesecake be = $y$

Given:

3 New York stile cheesecake and 7 apple cheese cake were sold for a total of $78.

Cost of 3 New York style cheesecake be = $3x$

Cost of 7 apple cheesecake be = $7y$

Total = $78

We have:

A) $3x+7y=78$

12 New York stile cheesecake and 12 apple cheese cake were sold for a total of $168.

Cost of 12 New York style cheesecake be = $12x$

Cost of 12 apple cheesecake be = $12y$

Total = $168

We have:

B) $12x+12y=168$

Dividing each term in equation B by 12.

$\frac{12x}{12}+\frac{12y}{12}=\frac{168}{12}$

$x+y=14$

Solving for $x$ in terms of $y$

Subtracting $y$ both sides.

$x+y-y=14-y$

$x=14-y$

Substituting $x=14-y$ in equation A.

$3(14-y)+7y=78$

Using distribution:

$42-3y+7y=78$

$42+4y=78$

Subtracting both sides by 42.

$42+4y-42=78-42$

$4y=36$

Dividing both sides by 4.

$\frac{4y}{4}=\frac{36}{4}$

∴ $y=9$

Substituting $y=9$ in $x=14-y$

∴ $x=14-9=5$

∴ Cost of one New York style cheesecake  = $5

∴ Cost of one apple cheesecake = $9