Question

I need an explanation of:There are 75 pennies, quarters, and dimes in a box.There are 4 times as many pennies as quarters.There are 3 more dimes than quarters.How many pennies are there in the box?

Answer 1

In this problem, you are given that there are 75 pennies, quarters, and dimes in a box. You can solve for the number of pennies by setting up equations based on the given information and then solving for the variables. The answer is that there are 40 pennies in the box.

Step-by-step explanation:

In this problem, you are given that there are 75 pennies, quarters, and dimes in a box. Let's represent the number of quarters as 'q', the number of dimes as 'd', and the number of pennies as 'p'.

We are given that there are 4 times as many pennies as quarters, so we can write the equation p = 4q.

We are also given that there are 3 more dimes than quarters, so we can write the equation d = q + 3.

Now, we can substitute the value of 'd' in terms of 'q' into the equation p = 4q to get p = 4(q + 3).

Finally, we substitute the value of 'p' from the previous equation into the given information that the total number of coins is 75, giving us the equation 4(q + 3) + q + (q + 3) = 75.

Simplifying the equation, we get 6q + 15 = 75.

Subtracting 15 from both sides, we find that 6q = 60.

Dividing both sides by 6, we get q = 10.

Since there are 4 times as many pennies as quarters, p = 4q = 4(10) = 40.

Therefore, there are 40 pennies in the box.

Answer 2

Let:

p = number of pennies (one cent)

q = number of quarters (25 cents)

d = number of dimes (10 cents)

The total number of coins in the box is 75, thus:

p + q + d = 75

This gives us the first equation.

We also know there are 4 times as many pennies as quarters, thus:

q = 4p

We also know there are 3 more dimes than quarters, thus:

d = q + 3

Since q = 4p:

d = 4p + 3

It's required to find the number of pennies in the box (p).

Substituting the last two equations in the first one:

p + 4p + 4p + 3 = 75

Simplifying:

9p = 72

Dividing by 9:

p = 8

There are 8 pennies in the box

To complete the answer, we find:

q = 4*8 = 32

d = 32 + 3 = 35

There are also 32 quarters and 35 dimes in the box