Question

Gabriella is selling cakes for a school fundraiser. Customers buy apple and merinque tarts. Castel sold 6 apple cakes and 4 lemon merinque cakes for a total of $ 80. Gabriella sold 6 apple cakes and 5 lemon merinque cakes for a total of $ 94. What is the cost of each merinque cake apple and lemon?

Answer 1

Cost of each apple cake is $4 and Cost of each Lemon merinque cake is $14.

Explanation:

Let the cost of each apple cakes be 'x'.

Let the cost of each lemon merinque cake be 'y'.

Now Given:

Castel sold 6 apple cakes and 4 lemon merinque cakes for a total of $ 80.

So we can say that;

6 times cost of each apple cakes plus 4 times cost of each lemon merinque cake is equal to $ 80.

framing in equation form we get;

`6x+4y=80` ⇒ Equation 1

Also Given:

Gabriella sold 6 apple cakes and 5 lemon merinque cakes for a total of $ 94.

6 times cost of each apple cakes plus 5 times cost of each lemon merinque cake is equal to $ 94.

framing in equation form we get;

`6x+5y=94` ⇒ Equation 2

Now subtracting equation 1 from equation 2 we get;

`6x+5y-(6x+4y)=94-80\\\\6x+5y-6x-4y=14\\\\y=\$14`

Substituting the value of y in equation 1 we get;

`6x+4y =80\\\\6x+4*14=80\\\\6x+56=80\\\\6x=80-56\\\\6x=24`

Dividing both side by 6 we get;

`(6x)/(6)=(24)/(6)\\\\x=\$4`

Hence Cost of each apple cake is $4 and Cost of each Lemon merinque cake is $14.