A bad contains pennies, nickels, dimes, and quarters. There are 50 coins in all. Of the coins, 14% are pennies are 32% are dimes. There are 4 more nickels than pennies. How much money does the bag contain?

The bag contains 7 pennies, 16 dimes, 11 nickels and 16 quarters and a total of $6.22

Step-by-step explanation:

Given

%

%

Nickel = 4 more than pennies

Required

How much money does the bag contain?

We start by calculating the number of pennies

% of total

So,

Also, % of total

The question says there are 4 more nickels than pennies;

This means

Recall that

So,

The question also says that the bag contains quarters;

If total coins is 50, then

Converting each of these to dollars

1 penny = $0.01

7 pennies = 7 * $0.01 = $0.07

1 nickel = $0.05

11 nickels = 11 * $0.05 = $0.55

1 dime = $0.10

16 dimes = $0.10 * 16 = $1.6

1 quarter = $0.25

16 quarters = $0.25 * 16 = $4

Total = $0.07 + $0.55 + $1.6 + $4

Total = $6.22

Hence, the bag contains 7 pennies, 16 dimes, 11 nickels and 16 quarters and a total of $6.22

Part (a)

Let's replace x with 15 and evaluate to see if he is correct or not.

x/2 - 3 = 6

15/2 - 3 = 6

7.5 - 3 = 6  

4.5 = 6

We get a false statement after simplifying everything. We need to get the same number on both sides to get a true statement. Therefore, Ahmed is not correct.

Part (b)

Let's solve for x. We do so by first adding 3 to both sides, and then multiplying both sides by 2. This follows PEMDAS in reverse, undoing everything to isolate the variable.

x/2 - 3 = 6

x/2 = 6+3 add 3 to both sides

x/2 = 9

x = 9*2 multiply both sides by 2

x = 18 is the answer

As a check, we'll use the same idea as part (a)

x/2 - 3 = 6

18/2 - 3 = 6

9 - 3 = 6

6 = 6

We get a true statement this time. This confirms x = 18