Question

40 POINTS

Mike spent $12 on a bag
containing red and blue candies. The bag weighed 7 pounds. The red candy
costs $1.50 per pound and the blue candy cost $2 per pound. How much red and blue candy did Mike
have?

Use sentence to define your variables and final answer in a complete sentence.

Answer 1

Solution :-

Let the red candy be r and blue candies be b

r + b = 7(EQ 1)

1.5r + 2b = 12

2r + 2b = 14

Now,

(1.5r + 2b = 14) = (2r + 2b + 12)

2r - 1.5r = 14 - 12

0.5r = 2

r = 2/0.5

r = 4

Using equation 1

4 + b = 7

4b = 7

b = 7 - 4

b = 3

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Answer 2

• 4 red and 3 blue

Explanation:

Let red candy weighs r and blue candy weighs b

Total weight is 7 pounds:

• r + b = 7

Red costs $1.5 per pound, blue costs $2 per pound and total cost is $12

• 1.5r + 2b = 12

We have two equations.

Solve by elimination, double the first equation and subtract the second equation from the first:

• 2r + 2b = 14
• 1.5r + 2b = 12

Subtract and solve for r:

• 2r - 1.5r = 14 - 12
• 0.5r = 2
• r = 4

Find b using the first equation:

• b = 7 - r
• b = 7 - 4 = 3

The answer is:

• Mike had 4 pounds of red and 3 pounds of blue candies.