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How many cans of corn does he buy?

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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