Question

James and Amanda are selling cheesecakes for a school fundraiser. Customers can buy pecan cheesecakes and chocolate marble cheesecakes. James sold 12 pecan cheesecakes and 1 chocolate marble cheesecake for a total of $157. Amanda sold 3 pecan cheesecakes and 5 chocolate marble cheesecakes for a total of $101. What is the cost each of one pecan cheesecake and one chocolate marble cheesecake?

Answer 1

The cost of one pecan cheesecake is $12 and

the cost of 1 chocolate marble cheesecake is 13$

Explanation:

Let the cost of one pecan cheesecake be x

And the cost of one chocolate marble cheesecake be y

Now, James sold 12 pecan cheesecakes and 1 chocolate marble cheesecake for $157, we represent this as,

12x + y = 157 (i)

And, Amanda sold 3 pecan cheesecakes and 5 chocolate marble cheesecake for $101, we represent this as,

3x + 5y = 101 (ii)

now, we just need to solve these two equations to get the amounts,

since 12x + y = 157

y = 157 - 12x

putting value of y in (ii)

3x + 5(157-12x) = 101

3x +785 - 60x = 101

-57x + 628 = 101

-57x = 101 - 785

-57x = -684

multiplying by -1 on both sides,

57x = 684

x = 684/57

x = 12

Now, finding y using, y = 157 - 12x

since x = 12,

y = 157 - (12)(12)

y = 157 - 144

y = 13

So, the cost of one pecan cheesecake is $12 and the cost of 1 chocolate marble cheesecake is 13$