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

Answer:

we have 5 nickels and 7 dimes

Step-by-step 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