Question

the amount of money in cents in a jar containing some nickels and (d) dimes and some quarters if there are 8 times as many nickels as dimes and twice as many quarters as nickels.the expression for the amount of money in the jar is ______ cents

Answer 1

Let N be the number of nickels in the jar, D the number of dimes and Q the number of quarters in the jar.

Recall that a nickel is 5 cents, a dime is 10 cents and a quarter is 25 cents. So, the expression

$5\cdot N$

represents the total amount of cents we have, in nickels. In the same manner, we get the following expression for the dimes and the quarters

$10\cdot D$$25\cdot Q$

So, the total amount of cents we have in the jar would be the sum of these quantities. That is

$5N+10D+25Q$

This is one valid expression. However, we would like to write an equivalent one using the information we are given.

First, we are told that there are 8 times as many nickels as dimes. This means that if we take the number of dimes D and multiply it by 8, we get the number of nickels N. That is

$N=8\cdot D$

Also, we are told that we have twice as many quarters as nickels. That is that if we multiply by 2 the number of nickels, we get the number of quarters. So we have

$Q=2\cdot N$

Replacing the value of N that we found before, we have

$Q=2\cdot N=2\cdot(8\cdot D)=16D$

So now, we can replace all this values in our original expression. Thus, we end up with the expression

$5N+10D+25Q=5\cdot(8D)+10\cdot D+25\cdot(16D)=40D+10D+400D=450\cdot D$