Question 101002: I really do want to be able to understand how to understand and be able to write this equations. I have tried on my own and nothing, plus I also need to be able to also solve the problem.
I have twice as many nickels as quarters. If the coins are worth $4.90, how many quarters and nickels do I have?
Answer by bucky(2189)   (Show Source):
You can put this solution on YOUR website! You are dealing with unknown numbers of nickels and quarters. To help keep clear what is what,
let's use N to represent the number of nickels and Q to represent the number of quarters.
.
The problem tells you that you have twice as many nickels as quarters. That means that the
number of nickels is twice the number of quarters. In equation form this becomes:
.
N = 2*Q
.
Next we know that a nickel is 5 cents. So for every nickel you have 5 pennies. The total
number of pennies you have in nickels can be found by multiplying the number of nickels N
by 5. So in pennies from nickels we have 5*N pennies.
.
Similarly, we know that a quarter is 25 cents. So for every quarter you have 25 pennies. That
means that the total number of pennies you have from quarters can be found by multiplying
the number of quarters Q by 25. So from quarters we have 25*Q pennies.
.
Finally we know that $4.90 is 490 pennies.
.
So if we add the pennies from nickels to the pennies from quarters, the answer should be
490 pennies. In equation form this is:
.
5N + 25Q = 490
.
But earlier we said that N = 2Q. So in the "pennies" equation we can substitute 2Q for N
and when we do the pennies equation becomes:
.
5(2Q) + 25Q = 490
.
Multiply the 5*(2Q) to get 10Q and the equation reduces to:
.
10Q + 25Q = 490
.
Add the two terms on the left side of this equation to get:
.
35Q = 490
.
and finally, solve for Q by dividing both sides of this equation by 35 to get:
.
Q = 490/35 = 14
.
We now know that there are 14 quarters. And since there are twice as many nickels as
there are quarters, there must be 28 nickels.
.
Let's check that. 28 nickels at 5 cents per nickel gives 28*5 = 140 pennies which is $1.40.
And 14 quarters at 25 cents each gives 14*25 = 350 pennies or $3.50. Added together
these two amounts are $1.40 + $3.50 = $4.90. That's what it is supposed to be so our answer
is correct.
.
Hope this helps you to understand the problem a little better.
.
|
|
|
