Question

On Planet Galactica, common units of distance are alpha, beta, and gamma. 4 gammas equal 5 betas. 2 betas equal 3 alphas. How many alphas equal 1 gamma?

Answer 1

Answer:

1 gamma = 15/8 alphas

Step-by-step explanation:

so we start by finding out what 1 gamma and 1 beta equals.

we know 4 gammas = 5 betas so if we divide by four on both sides we get:

1 gamma = 5/4 betas. we can apply that same procedure to 2 betas = 3 alphas and get 1 beta = 3/2 alphas

we know that 1 gamma = 5/4 betas and 1 beta = 3/2 alphas so how many alphas = 5/4 betas? using a proportion of ((3/2)/1) = ((x)/(5/4)) we can find that 5/4 betas = 15/8 alphas

therefore we know 1 gamma = 15/8 alphas or 1 and 7/8 alphas