Question

A band has members . If the number of band members is multiplied by 4 and divided by 5, the result is 21 greater than a number which is 30 less than the number of band members. How many band members are there?

a) 35
b) 40
c) 45
d) 50

Answer 1

To solve this problem, we can set up an equation and solve for the number of band members. By following the given information and simplifying the equation step by step, we find that there are 45 band members.

Step-by-step explanation:

To solve this problem, let's first define the number of band members as x.

The given information tells us that if we multiply the number of band members by 4 and divide it by 5, the result is 21 greater than a number which is 30 less than the number of band members.

Translating this into an equation, we have (4x/5) = (x - 30) + 21.

Now, we can solve for x.

First, let's distribute the 4/5 to simplify the equation: 4x/5 = x - 30 + 21.

Next, let's combine like terms: 4x/5 = x - 9.

Now, let's multiply both sides of the equation by 5 to eliminate the fraction: 4x = 5(x - 9).

Distributing the 5, we get: 4x = 5x - 45.

Next, let's subtract 5x from both sides to isolate x: -x = -45.

Finally, let's divide both sides by -1 to solve for x: x = 45.

Therefore, the number of band members is 45.