Question

If three smiles equals 10 grins, and 6 grins equals 9 laughes, how many laughes does it take to equal 2 smiles

Answer 1

10 laughs

Explanation:

Let S = smiles

Let G = grins

Let L = laughs

If 3 smiles equals 10 grins:

⇒ 3S = 10G

If 6 grins equals 9 laughs:

⇒ 6G = 9L

Multiply the second equation by ⁵/₃ so that the number of grins is 10:

⇒ 6G × ⁵/₃ = 9L × ⁵/₃

⇒ 10G = 15L

Therefore:

⇒ 3S = 10G = 15L

⇒ 3S = 15L

Multiply by ²/₃:

⇒ 3S × ²/₃ = 15L × ²/₃

⇒ 2S = 10L

Therefore, 10 laughs equal 2 smiles.