Question

In an election for class officer, Steven beat his opponent, Tyler, in a 4 : 3 ratio. Steven had a total of 412 votes. How many people voted in the election?

Answer 1

721

Answer 2

How did you set up your equation?

Answer 3

i dont know i need help

Answer 4

In an election for class officer, Steven beat his opponent, Tyler, in a 4 : 3 ratio. Steven had a total of 412 votes. How many people voted in the election?

Answer 5

np. Ratios can be thought of as fractions, set up the right way. A 4 : 3 ratio means that 1) there are 7 "parts" of which Steve has four and Tyler has 3. So, Steve has 4 / (4+3) or 4/7 of the votes. So, if total votes are N, we have N x 4/7 = 412. N = (412)(7/4), which is the answer you got. It's important that you go through either this or similar reasoning to get the answer. You have mathematical ability, maybe you are not just going through all the steps systematically. You did something right or you wouldn't have gotten the answer, so give yourself a lot of credit.

Answer 6

how do i set up the equation for tyler

Answer 7

You can use what I did as a model if you can think of the solution methodology in these terms. Note I said "these terms". This is why it is so absolutely essential for students to try it on their own first. It's not the formula or memorization. It's all about creative and critical thinking. That's where learning takes place. I'll help you with Tyler, but you will finish out the work. If Steve won 4:3, that means Tyler lost 3:4, so he has 3 of the 3+4=7 parts. He has 3/7. There, that's actually most of the work, believe it or not. Set up an N for Tyler and let's see what you get.

Answer 8

Hint: you now know the total votes cast for both candidates together. You know Tyler got 3/7 of them. That's a big, big hint.

Answer 9

2/5=x/21-x can you help me

Answer 10

If you are like most students who have difficulty with conceptualizing this type of problem, think of the fraction I gave as a percentage. You are setting up an equation. You have 721 total votes. You are basically looking for the correct mathematical operation.

Answer 11

More help: Let T be the total votes. If I am interested in ascertaining what is 3/7 of that, then I am looking at dividing that by 7 and then taking 3 of those piles. I know this sounds basic and even childish, but it's not. It's conveying a thinking process. So, if you divide by 7 and take 3 of the piles, you are taking your initial number and multiplying it by 3/7.

Answer 12

T x fraction = The # of votes for the loser. T is 721 or T. fraction is 3/7.

Answer 13

Is this making sense to you?

Answer 14

yes can you help me with other equations

Answer 15

2/5=x/21-x

Answer 16

Is this equation a brand-new problem or is it related to the Tyler/Steve question?

Answer 17

new equation

Answer 18

Okay. You are solving for x. You have 2 terms with an x in them. You are shooting for getting one term with an x, but one has a 21 in the denominator. So, your attention gets drawn to the right side where it would be very good to get the x's "together". Try to get the x's together in a numerator with a common denominator. Big hint to start you off: a/b + a = a/b + (ab)/b= (a + ab)/b.

Answer 19

how do i do that

Answer 20

That -x, which is the same as adding a negative x, multiply it by 1 which is 21/21 (to match the denominator in the first term) to get -21x/21. That's the first step.

Answer 21

x=-1

Answer 22

So, you would get 2/5=x/21-x is the same as 2/5=x/21-21x/21. No, x is not -1. But we will get x soon. Are you with me so far with the new equation?

Answer 23

ok

Answer 24

Ok, your turn. Take the last equation and simplify the right side a little. Hint: a/b - c/b = (a-c)/b. We keep the denominator the same (keep it 21) and then you can subtract in the numerator. Let's see what you get.

Answer 25

so whats the numerator

Answer 26

In the expression a/b, a is the numerator. The numerator is what is on "top".

Answer 27

21-2

Answer 28

The right side is x/21 - 21x/21. The first "part" of the numerator is x and the second 'part" is -21x. The denominator is just 21. So the full numerator is x - 21x and the denominator is still just 21. So, the right side now looks like (x - 21x) / 21

Answer 29

Now we can get the x's "together" by combining the 2 terms in the numerator. How would you simplify x - 21x ?

Answer 30

x-x

Answer 31

x/21=21/x

Answer 32

I've got to get you to think through this one. We're going to use something concrete. If I have 6hamburgers and I take away 2hamburgers, what do I have left? Your answer should be in some # of hamburgers and will look like #hamburgers. Fill in the #

Answer 33

4 hamburgers

Answer 34

Good. In this equation, x works like hamburgers. So, what is x - 21x ? Hint: x - 21x = (1-21)(x). Simplify this further.

Answer 35

20x

Answer 36

Are you saying that 1-21 = 20 ? Are you sure?

Answer 37

-20

Answer 38

Good. So, (1-21)(x) = -20x. We are getting the right side simpler, but we're not all the way there yet. Our next simplification is done along with the left side. So, our equation is now: 2/5 = -20x. We can get x all by itself (and the answer) if we multiply BOTH sides by the same number. What number do we multiply the right side by so that it is x and not -20x ?

Answer 39

-20*21

Answer 40

Hint: if you have (a)(x) and you want x, multiply it by 1/a because (1/a) times (a)(x) = (1/1)x or just x. So, your "a" is -21. What do you multiply by?

Answer 41

-21

Answer 42

Is that in the form 1/a ? Remember, your "a" is -21. How do you write "one over -21" ?

Answer 43

1/-21

Answer 44

Good. How do we write 1/a if "a" is -20 ?

Answer 45

1/-20

Answer 46

Okay, so our equation, at this point, is 2/5 = -20x. Multiply both sides by 1/(-20). We know that the right side will be x. How do you multiply the left side by 1/(-20) ?

Answer 47

5(1)=2(-20)

Answer 48

I can't help you any more, I have to go.

Answer 49

okay but is that right

Answer 50

No, the problem is that you are having difficulty with arithmetic. You have to learn that before you can perform algebra and pre-algebra.

Answer 51

i have difficulties with math

Answer 52

I wish I could help you with your particular concerns, but I am not able to show you arithmetic. I am truly sorry. There is a special teaching technique for that and I don't think I can teach arithmetic. I can teach algebra and above.

Answer 53

okay