1.) the sum of two numbers is 17 and their difference is 29. What are the two numbers?
2.) John has $2.35 in nickels and dimes. If she has 33 coins in all, find the number of nickels and dimes.
THANK YOU SO MUCH!!! :))

Both of your questions involve something called "Systems of Equations" and should be a lesson you'll receive in an Algebra II course. I'll teach you the concept so you'll have it and can use it later whenever you need.

Whenever you're performing an algebraic action involving two unknown variables, you'll always find that there are two equations given. For instance, in your first question there are two equations:

x + y = 17
x - y = 29

In order to tackle this challenge, you need to perform three steps: (1) solve for one of the variables in the first equation (you can use either equation first...it doesn't matter), then (2) plug in the value for the "solved" variable into the second equation and solve for the second variable. After that, (3) plug in your concrete value from the second equation into either equation to find the concrete value for the first variable.

So let's try this. Step 1, we'll first try to solve for x in the first equation (you could solve for y -- it doesn't matter). I also chose to start with the first equation for your first question.

x + y = 17
x = 17 - y

That's as far as we can go, but we now have a formula for what "x" represents. Step 2, we now turn our attention to the second equation.

x - y = 29

Now, remember, we want to plug in the value of x that we figured out in the first formula, which was (17 - y). This will give you an equation with only one variable so it's more like the algebra that you're used to working. So:

x - y = 29
(17 - y) - y = 29
17 - 2y = 29
-2y = 12
y = -6

So now you know one concrete number: y equals -6. Now you move to step 3, which is to plug that value into either equation you want and solve for x. Let's pick the first equation just for fun:

x + y = 17
x + -6 = 17
x = 23

Your answer is x = 23, y = -6.

If you want to check your work, plug in both values into either equation and make sure they work.

x + y = 17
23 + (-6) = 17
23 - 6 = 17
17 = 17

x - y = 29
23 - (-6) = 29
23 + 6 = 29
29 = 29

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For your second question, we'll do the same thing. Your two questions are:

$0.05x + $0.10y = $2.35
x + y = 33

This assumes x to be nickles and y to be dimes. To begin, I'll start with the second equation to show you that it really doesn't matter which equation you start with.

x + y = 33
x = 33 - y

$0.05x + $0.10y = $2.35
$0.05(33 - y) + $0.10y = $2.35
$1.65 - $0.05y + $0.10y = $2.35
-$0.05y + $0.10y = $2.35 - $1.65
$0.05y = $0.70
y = $0.70 / $0.05
y = 14

x + y = 33
x + 14 = 33
x = 19

Answer is x = 19, y = 14.

Proof:

x + y = 33
19 + 14 = 33
33 = 33

$0.05x + $0.10y = $2.35
$0.05(19) + $0.10(14) = $2.35
$0.95 + $1.40 = $2.35
$2.35 = $2.35