Question

Mrs. Smith is shopping in a super market and she has a budget of $86 to spend on $5 cakes, $1 eggs, $18 pizzas. She wants to buy 20 items for the coming week and must buy as many eggs as cakes and pizzas combined. How many of each item should she buy? Write a system of equations to help you solve this problem.

Answer 1

c=#of cakes

e=#of eggs

p=#off pizzas

she has a budget of $86 to spend on $5 cakes, $1 eggs, $18 pizzas, we will express this into this equation:

5c+e+18p=86 (1)

and She wants to buy 20 items for the coming week will be express like this:        

c+e+p=20 (2)

must buy as many eggs as cakes and pizzas combined:            

e=c+p   (3)

we will need to replace equation (3) into (1)                  

c+c+p+p=20  

2c+2p=20

2p=20-2c

p=10-c   (4)

replace equation (4) into (1)

5c+c+p+18(10-c)=86

6c+p+180-18c=86

6c+10-c+180-18c=86

-13c=-104

c=8   p=2  e=10

8 cakes. 2 pizzas and 10 eggs

Answer 2

18 x 3 = 54
5 x 3 = 15
1 x 3 = 3