Math homework help!! Algebra in the let/then format?

Question

Algebra in the Let, then, format! Help!?
I really need help!! The format it's in is Let dimes (for example)=x, then nickels=x+6.. Both Let and then have to use the SAME VARIABLE! Then the work. And could you take me through it step by step? I'm really confused, and I have a test on it in a few days.

1) A jar contains $36.25 in dimes and quarters. There are 250 coins 'in the jar. How many quarters are in the jar?

2)In a pile of coins, there are 15 more quarters than loonies (A loonie is a one dollar coin). The total value of the coins is $21.25. How many quarters are there?

Additional Details

1 hour ago
NO!!!!!!!! I'm getting really REALLY REALLY frusterated now!!! I've asked this question 3 times! THE VARIABLE HAS TO BE THE SAME!!!!!!!! LIKE, LET quarters=x, and dimes=4x!!!! THEY HAVE TO BE THE SAME!!! I WOULD FAIL IF I USED DIFFERENT WAYS!

Answer 1

No need to get frustrated in advance.

1) A jar contains $36.25 in dimes and quarters. There are 250 coins in the jar. How many quarters are in the jar?

You can do this question all in dollars or all in cents. We will use cents because it's easier to use integers than decimals.

Let
q = number of quarters

Then
250 - q = number of dimes

Now write the equation that adds up the value of the coins.

25q + 10(250 - q) = 3625
25q + 2500 - 10q = 3625
15q = 3625 - 2500 = 1125
q = 1125/15 = 75

There are 75 quarters.
_____________________________

2) In a pile of coins, there are 15 more quarters than loonies (A loonie is a one dollar coin). The total value of the coins is $21.25. How many quarters are there?

Let
q = number of quarters

Then
q - 15 = number of loonies

Now write the equation that adds up the value of the coins.

25q + 100(q - 15) = 2125
25q + 100q - 1500 = 2125
125q = 2125 + 1500 = 3625
q = 3625/125 = 29

The number of quarters is 29.

Answer 2

In problem 1 the LET is not about the value of the quarters but the number of quarters.

LET x = the number of quarters. (this way x will be your answer when you solve the equation)

THEN 250-x = the number of dimes-- based on the info in the question. (For example if we had 10 quarters there would have to be 240 dimes.)

The next step is to write an equation for the situation. The number of quarters times 25 cents plus the number of dimes times 10 cents must equal $36.25

So, x*$0.25 + (250-x)*$0.10 = $36.25

Finally solve the equation.

First simplify the parenthesis
x*0.25 + 250*0.10 - x*0.10 = 36.25

x*0.25 + 25 - x*0.10 = 36.25

Subtract 25 from both sides

x*0.25 - x*0.10 = 11.25

Isolate x

x(0.25 - 0.10) = 11.25

Simplify

x(0.15) = 11.25

Divide by 0.15

x = 75
there are 75 quarters

Check

75 * 0.25 = 18.75 (The quarters)
(250 -75) * 0.10 = 17.50 (The dimes)

18.75 + 17.50 = 36.25

Does that help?????

Answer 3

Wow, Canadian math is complicated. Here in the USA, we can use "x" and "y"... it is easier that way. Sorry.

P.S.
Can you have a Quarter = 5x and a Dime = 2x (where x=5 cents)?