Question

Joni has two cats in the yard, Stephen and Graham. If both animals gained 20 pounds, Stephen would be 25% heavier than Graham. For what it’s worth, if they both lost 20 pounds, Stephen would be 50% heavier than Graham. How much does each animal weigh?

Answer 1

Stephen weighs 80 lbs

Graham weighs 60 lbs

Explanation:

Let Stephen the cat = S

Let Graham the cat = G

25% heavier = 125% = 125/100 = 1.25

50% heavier = 150% = 150/100 = 1.5

If both animals gained 20 lbs, S would be 25% heavier than G:

S + 20 = 1.25(G + 20)

⇒ S = 1.25(G + 20) - 20

⇒ S = 1.25G + 5

If both animals lost 20 lbs, S would be 50% heavier than G:

S - 20 = 1.5(G - 20)

⇒ S = 1.5(G - 20) + 20

⇒ S = 1.5G - 10

Equate both equations for S, and solve for G:

S = S

⇒ 1.25G + 5 = 1.5G - 10

⇒ -0.25G = -15

⇒ G = 60

Substitute found value for G into one of the equations for S and solve for S:

S = 1.5G - 10

⇒ S = 1.5 x 60 - 10

⇒ S = 90 - 10

⇒ S = 80

Stephen weighs 80 lbs

Graham weighs 60 lbs