Question

how do i solve this: twice as many dimes as nickels; value of dimes is .75 more than value of nickels. How many nickels?

Answer 1

You want to set up two equations. One giving value to the coins, the other accounting for the number of coins.
d=dimes
n=nickels
So first, the number of each:
since you have twice as many dimes as nickels, if you multiply your number of nickels by 2, you'll get your number of dimes. So 2n=d.
Your second equation would deal with value. A dime is worth 10 cents, so 10d=value of a dime and 5n=value of a nickel. Value of nickels + .75 =value of dimes. So 10d=5n+75.
Now solve your two equations by substituting 2n for d in your second equation since 2n=d.
So 10d=5n+75
10(2n)=5n+75
20n=5n+75
15n=75
n=5
Now that you know you have 5 nickels, plug into your equation and solve for d.
2n=d
2(5)=d
d=10
So you have 10 dimes and 5 nickels.

Answer 2

thx!