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 you solve this problem.

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

add all the numbers and check the ones place.

the answer is 486. as the ones place is more than 4, the estimation will be the next 10 ie, 490