Three-fourths of seven less than a number is forty-two. Find the number.

- anonymous

Three-fourths of seven less than a number is forty-two. Find the number.

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- anonymous

my ans is -147/4

- anonymous

(3/4)(x-7) = 42. Gogogo

- anonymous

\[\frac{3(x-7)}{4} = 42 \rightarrow \frac{4(42)}{3} = x-7 \rightarrow x=?\]

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## More answers

- anonymous

so the number is 49?

- anonymous

Close..
\[ x-7 = 56 \rightarrow x-7+7 = 56 +7 = x = ?\]

- anonymous

63?

- anonymous

Indeed.

- anonymous

ok i got another for you...i like your help

- anonymous

The real trick here is in setting up the problem initially. Being able to convert word problems into workable equations is a good talent to develop.

- anonymous

suzette did twice as many pushups as mark did. bonnie did five less pushups than mark did. if they did 71 pushups together how many did each do?

- anonymous

\[\text{Polpak I prefer } \implies\ \text{instead of} \rightarrow\]
The latter looks to much like a limit.

- anonymous

Let S be the number of pushups Suzette did, and M be the number Mark did, and B is the number Bonnie did.
Translate this sentence into an equation.
"They did 71 pushups altogether."

- anonymous

Newton: \[ \lim_{n \rightarrow 0}\] Looks like a limit \[ \rightarrow \] doesn't. Not to me anyway. And in my homework I always use a single arrow instead of the double thing, so it feels more natural to me.

- anonymous

\[2s +m=5-m=71 ?\]

- anonymous

That's a bit of a leap. Try just using the variables I defined. If they all did 71 pushups then:
\[ M + S + B = 71\]

- anonymous

Then we look at how M, S, and B are otherwise related.

- anonymous

"Bonnie did 5 less pushups then Mark"
\[ \rightarrow B = M-5\]

- anonymous

"Suzzette did twice as many pushups as mark"
\[ \rightarrow ?\]

- anonymous

2(m)=s

- anonymous

Right.
Now, using what we know about S and B, we can go back to our original equation and find how many mark did.
\[ M+S+B=71\]
Using the fact that S=2M
\[ \rightarrow M + 2M + B = 71\]
Using the fact that B=M-5
\[ \rightarrow ?\]

- anonymous

im lost

- anonymous

I plugged in 2M for S in the M + S + B = 71 equation. Now do the same for B.

- anonymous

m-5=b

- anonymous

Yes, that's the equation for what B _is_. Now use that in the equation
M + S + B = 71

- anonymous

im so confused

- anonymous

B = M - 5.
Would you agree then that M + S + B = M + S + (M-5) ?

- anonymous

ok

- anonymous

And since S = 2M
Would you agree that M + S + (M-5) = M + 2M + M - 5 ?

- anonymous

i think

- anonymous

\[ S = 2M \]
\[\rightarrow M + S = M + 2M \]
\[ B = M-5\]
\[ \rightarrow M + S + B = M + S + (M-5) \]
\[ = (M + S) + (M-5) = M + 2M + M-5\]

- anonymous

Does that make sense?

- anonymous

not at all

- anonymous

S = 2M
S + 5 = 2M + 5 right?

- anonymous

If S = 2M
then S + SOMETHING = 2M + SOMETHING

- anonymous

That is what equals means

- anonymous

I don't understand what you're not understanding. Which part is confusing?

- anonymous

im a retard when it comes to math...i dnt even know where to begin to solve ur problem

- anonymous

Do you understand what S = 2M means? It means that anywhere you have an S, you can replace it with a 2M and it will mean the same thing.

- anonymous

ok
i understand that

- anonymous

So if we have an equation
M + S + B = 71, we can replace the S with 2M right?

- anonymous

yea

- anonymous

So rewrite the equation by replacing the S. Also replace the B since we know that B = M-5.

- anonymous

M+2(M)=71?

- anonymous

Not quite.
M + 2M = 71 is the same as saying M + S is 71. But we know that's not true because M + S + B is 71 and B is not 0.
M + 2M + B = 71 is true. But since we know B = M-5 we can replace B in this equation and we get?

- anonymous

M+2M+M-5

- anonymous

Right. Now, since we said that
M + S + B = 71
and we said that
M + S + B = M + 2M + M - 5
Then we know that
M + 2M + M - 5 = 71
So solve for M.

- anonymous

32m 16s 23b

- anonymous

?

- anonymous

thats not right

- anonymous

\[ M + 2M + M -5 = 71\]
\[ \rightarrow 4M -5 = 71 \]
\[ \rightarrow 4M = 76 \]
\[ \rightarrow M = 76/4 \]
\[ \rightarrow M = 19 \]

- anonymous

38 19 14

- anonymous

S = 2M = 2(19) = 38
B = M-5 = 19-5 = 14

- anonymous

the sum of three numbers is -48. the first number is 12 more than the secong number, andthe third number is 20 less than twice the second number. find the three numbers.

- anonymous

Ok. This one you're gonna need to put more of the effort into. First pick variables for each of your 3 numbers (A, B, C?). Then take each sentance and see what it's telling you about your numbers. (Try to write the sentance as an equation)

- anonymous

The first sentance is:
The sum of the three numbers is -48. So your equation is ?

- anonymous

a+b+c=-48

- anonymous

Perfect. Now the next sentence.
The first number is 12 more than the second.
Therefore?

- anonymous

A=12+B

- anonymous

And finally,
The third number is 20 less than twice the second number.

- anonymous

C=20-2(b)

- anonymous

Not quite.

- anonymous

2B = twice the second number.
twenty less than twice the second number
= twenty less than 2B
= 2B - 20
If 2B is 10, than 20 - 10 is not twenty less than 10.

- anonymous

20-2(b)=C

- anonymous

No.

- anonymous

C = 2B - 20

- anonymous

ok

- anonymous

?

- anonymous

So now put them all together.
You have 1 equation with all 3 elements, and 2 other equations that give you replacement values for A and C. So replace them in and solve for B.

- anonymous

once again im lost

- anonymous

A + B + C = -48
A = 12 + B
So..
? + B + C = -48
Fill in the ?

- anonymous

36

- anonymous

... No
A = 12 + B.
So
(A) + B + C = (12+B) + B + C right??

- anonymous

ya

- anonymous

If A + B + C = -48
and A = 12 + B
and C = 2B - 20
the (A) + B + (C) = ?

- anonymous

Just replace the A and the C.

- anonymous

with what?

- anonymous

With what they equal.

- anonymous

i cant tell you what a equals without knowing b

- anonymous

............... You do know what A equals. A equals 12 + B. Period. It may also be represented in a different way, but you at least know that much.

- anonymous

So put 12 + B where there is an A. And put 2B-20 where there is a C.

- anonymous

12+b+2b-20

- anonymous

Right. And what does that equal again?

- anonymous

=-48

- anonymous

So what does B equal ?

- anonymous

Actually that's not quite right.

- anonymous

-8

- anonymous

you have 12 + B + 2B - 20 which equals (12+B) + (2B-20) which equals A + C. You forgot the B in the middle.

- anonymous

Rewrite the equation again.
A + B + C = -48, A = B + 12, C = 2B-20
So...

- anonymous

idk man

- anonymous

im dying here

- anonymous

A + B + C = (12+B) + B + (2B-20)
^A + ^B + ^C
Right?

- anonymous

yea

- anonymous

So if A + B + C = -48, what is B.

- anonymous

-36

- anonymous

\[12 + B + B + 2B - 20 = -48\]
\[\rightarrow 4B - 20 + 12 -12 + 20 = -48 - 12 + 20 \]
\[\rightarrow 4B = -60 + 20\]
\[\rightarrow 4B = -40\]
\[\rightarrow B = -10\]
\[\rightarrow A = 12 + B = 12 + -10 = 2 \]
\[\rightarrow C = 2B-20 = -20 -20 = -40 \]

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