Problem Solving

BTGModeratorVI wrote: ↑

Sun Aug 02, 2020 6:53 am

At a certain pizzeria, 1/8 of the pizzas sold in one week were mushroom and 1/3 of the remaining pizzas sold were pepperoni . If n of the pizzas sold were pepperoni, how many were mushroom?

(A) (3/8)n
(B) (3/7)n
(C) (7/16)n
(D) (7/8)n
(E) 3n

Answer: B
Source: Official guide

Let T = the total number of pizzas sold

1/8 of the pizzas sold in one week were mushroom
So, T/8 = the total number of mushroom pizzas sold

Aside: 7T/8 pizzas are still unaccounted for.

1/3 of the remaining pizzas sold were pepperoni
So, 1/3 of 7T/8 = number of pepperoni pizza sold
Another words, 7T/24 = number of pepperoni pizza sold

If n of the pizzas sold were pepperoni, how many were mushroom?
In other words, 7T/24 = n

IMPORTANT: We already know that T/8 = the total number of mushroom pizzas sold
So, our job now is to take the equation 7T/24 = n and rewrite it so that we can determine the value of T/8

Take: 7T/24 = n
Multiply both sides by 3 to get: 7T/8 = 3n
Now divide both sides by 7 to get: T/8 = 3n/7

Answer: B

Cheers,
Brent

BTGModeratorVI wrote: ↑

Sun Aug 02, 2020 6:53 am

At a certain pizzeria, 1/8 of the pizzas sold in one week were mushroom and 1/3 of the remaining pizzas sold were pepperoni . If n of the pizzas sold were pepperoni, how many were mushroom?

(A) (3/8)n
(B) (3/7)n
(C) (7/16)n
(D) (7/8)n
(E) 3n

Answer: B
Source: Official guide

Solution:

We can let the total number of pizzas = x

We are given that 1/8 of the pizzas sold in one week were mushroom, which we can represent as (1/8)x.

Next we are given that 1/3 of the remaining pizzas sold were pepperoni and that n of the pizzas sold were pepperoni. Since 1/8 of the pizzas were mushroom, 1 - 1/8 or 7/8 of the pizzas were the remaining pizzas. Thus:

1/3(7/8)x = n

(7/24)x = n

x = (24/7)n

Since x = (24/7)n, the number of mushroom pizzas sold was (1/8)(24/7)n = (24/56)n = (3/7)n

Answer: B