Question

Destiny buys 3 tops and 4 bottoms for $160. The next day, she buys 6 tops and 1 bottom for $145. How much does each top and each bottom cost?

a) Tops: $15, Bottoms: $25
b) Tops: $20, Bottoms: $15
c) Tops: $25, Bottoms: $20
d) Tops: $15, Bottoms: $20

Answer 1

The cost of each top is $20, and the cost of each bottom is $25. We used a system of linear equations to find the value of the tops and bottoms using the elimination method.

Step-by-step explanation:

To solve the problem of finding the cost of each top and each bottom, we'll need to set up a system of equations based on the information provided:

• 3 tops + 4 bottoms = $160
• 6 tops + 1 bottom = $145

We'll denote the cost of one top as T and the cost of one bottom as B. This gives us the following equations:

1. 3T + 4B = 160
2. 6T + B = 145

Now, we can solve this system using the substitution or elimination method. Let's use elimination. We can multiply the second equation by 4 to align the coefficients for B with the first equation:

1. 3T + 4B = 160
2. 24T + 4B = 580

Subtract the first equation from the modified second equation:

24T + 4B - (3T + 4B) = 580 - 160

21T = 420

T = 20 (Divide both sides by 21)

Now, we substitute T = 20 into the second original equation:

6(20) + B = 145

120 + B = 145

B = 25 (Subtract 120 from both sides)

Thus, the cost of each top is $20 and the cost of each bottom is $25.