Question 188521This question is from textbook McDougal Littell Algebra 1
: Laura has $4.50 in dimes and quarters. She has 3 more dimes than quarters. How many quarters does she have.
How do you find two linear equations (y=mx+b), one that shows quantity of the coins. And one that shows the amount the coins are worth. I am suppose to use "d" and "q" to represent the dimes and quarters.
So far I got: q=dx+3 and 4.50=qx+d
This question is from textbook McDougal Littell Algebra 1
Found 2 solutions by solver91311, feliz1965:
Answer by solver91311(24713)   (Show Source):
You can put this solution on YOUR website!
I have no intention of being mean about this, but you are so far off track that the only way to get you back on the right path is to start from the beginning.
When you were told to create an equation in the form  , you were meant to use q and d in place of the variables y and x. I think that bit of instruction turned out to be more confusing than helpful.
Let d represent the number of dimes and let q represent the number of quarters. We know that she has 3 more dimes than quarters. So if you add 3 to the number of quarters you would get the number of dimes.
(just to keep track of the whole thing, notice that the equation that we just developed is in that very form if you consider the d to be the y, the understood 1 coefficient in front of the q to be the m, the q to be the x, and the 3 to be the b)
That takes care of the equation representing the relationship of the number of coins, so now let's look at an equation that represents the value of those coins. By the way, when I do coin problems, I like to change the dollars and cents representation into just cents, that is for this problem I'm going to represent the $4.50 as 450 cents. That will allow us to use whole number coefficients instead of decimal fractions. I just think it is neater. Having said that, onward.
Each dime is worth 10 cents, so d dimes must be worth 10d cents. Similarly q quarters must be worth 25q cents. And the total value of her money is 450 cents, so:
Now you could put this into form, thus:
But I think that is just uglier than a mud fence and of no real value to solving this problem, so let's just go back to the original value equation:
Since we know from earlier that  , we can substitute  for d in the value equation, like this:
 + 25q = 450)
Distribute:
Collect terms:
Divide by 35:
So Laura has 12 quarters, and 12 + 3 = 15 dimes.
Check the answer.
12 quarters = 
15 dimes = 
And  . Answer checks.
John
Answer by feliz1965(151)  (Show Source):
You can put this solution on YOUR website! Laura has $4.50 in dimes and quarters. She has 3 more dimes than quarters. How many quarters does she have?
Let x = number of coins
The value of a dime = 0.10
The value of a quarter = 0.25
I will use whole numbers in place of decimals for easy reading.
10(x + 3) + 25x = 450
25x = quarters
10(x + 3) = dimes
10x + 30 + 25x = 450
35x = 450 - 30
35x = 420
x = 420/35
x = 12
There are 12 quarters.
How many dimes?
dimes = 10(12 + 3)
dimes = 10(15)
dimes = 150
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