Question

Two friends visited a taffy shop. Rachel bought 4 pounds of strawberry taffy and 6 pounds of banana taffy for $44. Next, Pablo bought 2 pounds of strawberry taffy and 5 pounds of banana taffy for $30. How much does the candy cost?

Answer 1

Each pound of strawberry taffy and banana taffy costs $5 and $4 respectively

Explanation:

Lets assume the price of one pound of strawberry taffy to be x

And

The price of one pound of banana taffy to be y

If 4 pounds of strawberry taffy and 6 pounds of banana taffy costs $44

And

2 pounds of strawberry taffy and 5 pounds of banana taffy costs $30.

The above will lead to a simultaneous equation that looks like this

4x + 6y = 44

From the first equation, we can divide through by 2 and we get

2x + 3y = 22_______equation 1

2x + 5y = 30_______ equation 2

From equation 1,we make x the subject of the formula and we get

X = (22 - 3y)/2

Apply the above in equation 2 and we have

2[(22 - 3y)/2] + 5y = 30

We expand the above equation

(44 - 6y)/2 + 5y = 30

(44 - 6y + 10y)/2 = 30

44 - 6y + 10y = 60

4y = 16

Y= $4(price of a pound of banana taffy)

Now substitute y = 4 in equation 1 and we have

2x + 3(4) = 22

2x + 12 = 22

X = 10/2

X = $5(price of each pound of strawberry taffy)

Answer 2

The cost of the candy is

$5 for strawberry taffy and

$4 for banana taffy

Explanation:

Here we have

Let the strawberry taffy be = S and

the banana taffy = B

The system of equation becomes

4·S + 6·B = $44......................(1)

2·S + 5·B =$30.......................(2)

To solve the equations, we multiply equation (2) by 2 to get

2×(2·S + 5·B) =$30. × 2

4·S +10·B = $60.......................(3)

We subtract equation (1) from equation (3) to get

(4·S +10·B)-(4·S + 6·B) = $60 - $44

4·B = $16 or B = $16/4 = $4

Therefore, from equation (2) we have

2·S + 5×$4 =$30 or

2·S = $30 - $20 = $10

S = $10/2 = $5

The candy costs

Strawberry taffy = $5 and

Banana taffy = $4