Question

Jim has a total of 12 dimes and nickels worth a total of $0.95. If dimes are represented by d and nickels are represented by n, how would you represent the value of the money?

Answer 1

we have 5 nickels and 7 dimes

Explanation:

We have a total of 12 coins; n nickels and d dimes. So, the nickels and dimes that I own are 12 altogether or:

`n + d =12`

My second piece of information tells me that the value of my coins equals $0.95 We know that a nickel is worth $0.05 and a dime is worth $0.10:

`0.05n + 0.10d = 0.95`

So our systems of equations are as follows:

`\left \{ {{n + d =12} \atop {0.05n + 0.10d = 0.95}} \right.`

we solve for d and remplace in the second equation

`d=12-n`

`0.05n + 0.10(12-n) = 0.95`

isolate n an we get:

`0.05n + (12*0.10)-0.10n = 0.95\\`

`0.25=0.05n`

`n=5\\`

and we replace n=5 in the first equation:

`d =12-5=7`

we have 5 nickels and 7 dimes