Question

A plant costs p dollars and a bush costs b dollars. Ana buys 2 plants and 4 bushes for $42. Paola buys 7 plants and 9 bushes for $107. Write down a pair of simultaneous equations and solve them to find out the value of p and the value of b.

Answer 1

p = 5 and b =8

Explanation:

2p + 4b = 42

2p = 42 - 4b

p = 21 - 2b

7p + 9b = 107

7 (21 - 2b) + 9b = 107

147 - 14b + 9b = 107

147 - 5b = 107

-5b = -40

b = 8

2p + 4 * 8 = 42

2p + 32 = 42

2p = 10

p = 5

Answer 2

p = 5 and b = 8

Explanation:

First, create a system of equations:

2p + 4b = 42

7p + 9b = 107

Solve by elimination by multiplying the top equation by -7 and the bottom equation by 2:

-14p - 28b = -294

14p + 18b = 214

Add these together, and solve for b:

-10b = -80

b = 8

Plug in 8 as b into one of the equations, and solve for p:

2p + 4b = 42

2p + 4(8) = 42

2p + 32 = 42

2p = 10

p = 5

So, p = 5 and b = 8