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## How many cans of corn does he buy?

Alex Stocks up for the winter. He buys 32 cans of Vegetables. He buys 80 cents per can for tomatoes and 40 cents per can of corn, for a total cost of \$18.0
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# 3 Answers

If C is the number of cans of corn and T is the number of cans of tomatoes

C + T = 32     Equation 1

We also know that

(\$0.40)C + (\$0.80)T = \$18.00     Equation 2

We can replace the C in Equation 2 with (32 - T), or the T in Equation 2 with (32 - C).

(\$0.40)C + (\$0.80)T = \$18.00 = (\$0.40)(32 - T) + (\$0.80)T = \$18.00

We now have a solvable equation for T:

\$12.80 - (\$0.40)T + (\$0.80)T = \$18.00

T(\$0.80 - \$0.40) = \$18.00 - \$12.80 = \$5.20

(\$0.40)T = \$5.20

T = 13

C = 32 - 13 = 19

CHECK RESULT:

Does (\$0.40)(19) + (\$0.80)(13) = \$18.00?

Does \$7.60 + \$10.40 = \$18.00?

YES!!!

Let number of corn cans = x and number of tomatoe cans be y

x + y = 32

0.80y + 0.40x = 18

Eliminate y

y = 32 - x

substitute in second equation

0.8(32 - x) + 0.4x = 18

19 + y =

25.6 - 0.8x + 0.4x = 18

-0.4x = - 7.6

x = 19 = cans of corn

substitute x = 19 in first equation

19 + y = 32
y=13 = cans of tomatoes
:)
Hi Alyssa;
TOTAL COST...\$18.00
COST PER CAN OF TOMATO...\$0.80
COST PER CAN OF CORN...\$0.40
TOTAL QUANTITY OF CANS...32
x=quantity of cans of tomatoes
32-x=quantity of cans of corn
18.00=[(0.80)(x)]+[(0.40)(32-x)]
18.00=0.80x+12.80-0.40x
18.00=0.40x+12.80
Let's subtract 12.80 from both sides...
5.2=0.40x
13=x=quantity of cans of tomatoes
32-13=19=quantity of cans of corn
Let's check our work...
18.00=[(0.80)(x)]+[(0.40)(32-x)]
18.00=[(0.80)(13)]+[(0.40)(19)]
18.00=10.40+7.60
18.00=18.00