Please help me with my math homework!!!?

Question

okay, i cannot understand some of my math problems, please help me, do it step by step or i will not understand it.

Vita has 3 times as many dimes as quarters. The dollar amount of her dimes and quarters is $6.05. How many quarters does she have?

Sam has 4 times more dimes than quarters in his coin collection. He has 65 half dollars. The face value of his half dollars is half the face value of the dimes and quarters combined. How many dimes does he have? How many quarters does he have?

I need an equation for each of these

Answer 1

Alright, here we go.
You have three times as many dimes as quarters, so your dime quantity is just that: x = number of quarters, 3x = number of dimes.

Next, we need to consider dime and quarter values, so your dime and quarter values will be just that too: dimes = .10(3x) and quarters = .25(x)

So now we get .10(3x) + .25x = $6.05.
Combine like terms: .30x + .25x = .55x = $6.05
and solve: x = 11, 3x = 33. We have 11 quarters and 33 dimes.

Don't fall into the x,y trap. In algebra, everything is relative to something else, so keep it simple. If you have a multiple of something else for the quantity of another, just use a number for the coefficient like we did here. We had 3 times as many dimes as quarters, so we used 3x for the dimes and x for the quarter. Again, keep it simple and restate your objective - finding the total coin value, so we included price as factors. .10(3x) = dime value .25x = quarter value. AGAIN, keep it simple!(yes, it's silly now) .30x +.25x = .55x which equals the sum! $6.05!

I'm gunna let u do the second one but heres the hint. It's two parts (don't do it all at once)! Start out by finding the value of the half-dollars, then find the rest of the coins collective value. Put them together to see how much the whole collection is. Then, ASSIGN a quantity to each coin (dimes were 3x in the last problem, so how much are they worth in this problem). Next, assign a value to each coin (dimes were .10(3x) before, so how much are they now). Do this for every coin and don't make it too hard (if the problem tells you how many half dollars you have, then why are you trying to figure that out?).