Question

Trip has 15 coins worth 95 cents.Four of the coins are each worth twice as much as the rest.Construct a math argument to justify the conjecture that Trip has 11 nickles and 4 dimes.

Answer 1

Let's assign x to the value of one coin. Since four coins are twice the value of x, we'll have the term
`4(2x)` or
`8x` for these coins. The rest of the eleven coins have the value of x thus we'll have
`11x` as one of the terms, too.

If we add these two terms, we should get a sum of $0.95 since that's the total worth of Trip's coins. We can then solve for x to find how much each of the 11 coins of Trip are worth.


`8x+11x=0.95`

`19x=0.95`

`x=0.05`

Since 11 coins of Trip are worth $0.05 each, we have successfully verified that Trip has 11 nickles. Furthermore, the 4 remaining coins would automatically be dimes since it's twice the value of nickel.