Question

16. A collection of dimes and nickels is worth $3.10. If there are 45 coins in all, how many of each kind of coin are there?

Answer 1

To find the number of dimes and nickels in a collection worth $3.10 with a total of 45 coins, we can set up a system of equations using the total number of coins and their combined value.

Step-by-step explanation:

To solve this problem, we can set up a system of equations. Let's denote the number of dimes as 'd' and the number of nickels as 'n'. We know that there are 45 coins in total, so we can write the equation: d + n = 45.

We also know that the value of the dimes and nickels combined is $3.10. Since a dime is worth 10 cents and a nickel is worth 5 cents, the equation for the value can be written as: 10d + 5n = 310.

We can now solve this system of equations using substitution or elimination to find the values of 'd' and 'n'.

Answer 2

28 nickels and 17 dimes

Step-by-step explanation:

A nickel is worth 5 cents and a dime is worth 10 cents

If there are X nickels and Y dimes

Total value = 5X + 10Y cents

$3.10 == 3.10 x 100 = 310 cents

So 5X + 10 Y = 310

Divide both sides by 5 to get

5X/5 + 10Y/5 = 310/5

X + 2Y = 62 (1)

The total number of coins is X + Y and is given to be 45

X + Y = 45 (2)

Subtract Eq(2) from Eq(1) to get

X + 2Y - (X + Y) = 62-45 = 17

X + 2Y - X - Y = 17

Collecting like terms

(X - X) + (2Y - Y) = 17

Y = 17

So number of dimes = 17

To find X, the number of nickels use equation (2)

X + 17 = 45

Subtract 17 from both sides

X + 17 - 17 = 45 - 17

X = 28

So number of nickels = 28