Question

James has $10 in 5-cent and 10-cent coins in his change jar and counts 157 coins in total. How many 10-cent coins does he have?

Answer 1

46

Explanation:

You would have 46 10-cent coins. First split it up into dollars, there are $10 and 10 dimes in each dollar. So if James has 157 coins you would need to first see how many coins he has in total. In total there are 100 dimes. We need to get to 157 coins so we'll need to break up some of the coins. So we keep turning the dimes into nickels until we get the number 157 for all the coins in total. So James has 46 10-cent coins.

Answer 2

Explanation:

Let the number of 5-cent coins he has be x and the number of 10-cent coins he has be y

x coins + y coins = 157 coins

(x × 5)cents + (y × 10)cents = $10

These two equations are true about the money he has, i.e

x + y = 157

5x + 10y = 1000

(We made the $10 into 1000 cents because the coins are in cents)

We can solve the above equations either simultaneously or through substituting.

Simultaneously:

(x + y = 157) × 5

5x + 10y = 1000

5x + 5y = 785

5x + 10y = 1000

Subtract the co-efficients in the equations

0x + -5y = -215

-5y = -215

y = 43

This means he has 43 10-cent coins.

PS: We get the number of 5-cent coins by subtracting 43 from 157, the total number of coins he has.

Substituting:

x + y = 157

5x + 10y = 1000

y = 157 - x

5x + 10(157 - x) = 1000

5x + 1570 - 10x = 1000

-5x = -570

x = 114 coins

157 - 114 = 43 coins

Thus there are 43 10-cent coins.