Question

Jamar finds some nickels and quarters in his change purse. How much money (in cents) does he have if he has 4 nickels and 11 quarters? How much money (in cents) does he have if he has n nickels and q quarters?

Answer 1

Jamar has 295 cents with 4 nickels and 11 quarters. For any number of n nickels and q quarters, the total in cents is calculated by the formula (n × 5) + (q × 25).

Step-by-step explanation:

To determine how much money Jamar has in cents with his nickels and quarters, we first need to know the value of each coin. A nickel is worth 5 cents, and a quarter is worth 25 cents. If Jamar has 4 nickels and 11 quarters, we can calculate his total amount as follows:

• Value from nickels: 4 nickels × 5 cents per nickel = 20 cents
• Value from quarters: 11 quarters × 25 cents per quarter = 275 cents

Adding these together, Jamar has 20 cents + 275 cents = 295 cents in total.

For a general case where Jamar has n nickels and q quarters, the formula to calculate the total money in cents would be:

Total money in cents = (n × 5) + (q × 25)

This formula involves higher order addition and basic multiplication, which are part of money problems that require the ability to convert between cents and dollars.

Answer 2

1 nickel is worth 5 cents and 1 quarter is worth 25 cents.

So, if he has 4 nickels, this is worth 4 times 5 cents and if he has 11 quarters, this is worth 11 times 25 cents.

Both are worth the sum of these, so:

`4\cdot5+11\cdot25=20+275=295`

So, he has 295 cents.

If he has n nickels and q quarters, he has 5 times n plus 25 times q worth, so he has:

`5n+25q`