Question

A bag contains 120 marbles, some red, and the rest are black. There are 14 marbles for every black marble. How many red marbles are in the bag? Explain your reasoning.

a) 80
b) 90
c) 100
d) 110

Answer 1

Using the ratio of 14 to 1 for red to black marbles in a bag of 120 marbles, we calculate that there are 8 black marbles and 112 red marbles in the bag.

Step-by-step explanation:

To find how many red marbles are in the bag, we can use the information that there are 14 marbles for every black marble in a bag of 120 marbles. Let's denote the number of black marbles as b. The red marbles can then be expressed as 14b. Since the total number of marbles is the sum of black and red marbles, we can write the equation:

14b + b = 120

Simplifying this, we get 15b = 120. To find the value of b, we divide 120 by 15:

b = 120 ÷ 15

b = 8

So, there are 8 black marbles in the bag. To find the number of red marbles, we multiply the number of black marbles by 14:

Red marbles = 14 × b = 14 × 8 = 112

Therefore, the number of red marbles in the bag is 112, which means the correct option is not listed among the provided choices.