**Equation 1**

**Equation 2**

**T = 13**

**C**= 32 - 13 =

**19**

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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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

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

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

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