Phuong has $2.00 in nickels and dimes. The number of dimes is five more than twice the number of nickels. How many of each type of coin are in his bank?

Question

I don't know how to write an equation (two equations) for this

Answer 1

Let x = number of nickels and y = number of dimes.

Make sure you put the value of the nickel (.05) next to x and the value of the dime (.10) next to the y equivalent.

 

1) Cost equation: x(.05) + y(.10) = $2.00

 

2) Quantity equation: number of nickels is x. Number of dimes (y) is twice nickels (so 2x) plus five (+5).

 

To review:

 

Number of Nickels= x

Number of dimes = 2x + 5

 

Now, plug this into the cost equation.

 

x(.05) + (.10)(2x + 5) = 2.00

 

.05x + .20x + .50 = 2.00

.25x + .50 = 2.00

        - .50      .50

.25x = 1.50

 

Divide both sides by .25

 

x = 6

 

Remember that x = number of nickels and 2x + 5 = number of dimes

6 nickels and 2(6) + 5 = 17 dimes.

 

 

 

 

Answer 2

First, write equations from your information.  Let's use N for number of nickels and D for number of dimes.

 

1. .10*D+.05*N=2.00 ~ This is your basic money equation.  It looks easier if you multiply the entire thing by 100
1. 10D+5N=200
2. D=5+2N ~ Dimes equals 5 more than twice the nickels

 

Now you need to substitute one of these equations into the other.  It's easiest to plug #2 into #1, since it's already solved for D.

 

• 10(5+2N)+5N=200
• 50+20N+5N=200
• 25N=150
• N=6
• D=5+2N=5+2(6)=5+12=17

 

So 6 nickels and 17 dimes.  Let's see if this works.  6(.05)+17(.10)=2.00, so that's good.  And 2(6)+5=17, so that's good too.