Question

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

Answer 1

my ans is -147/4

Answer 2

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

Answer 3

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

Answer 4

so the number is 49?

Answer 5

Close..

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

Answer 6

63?

Answer 7

Indeed.

Answer 8

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

Answer 9

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.

Answer 10

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?

Answer 11

\[\text{Polpak I prefer } \implies\ \text{instead of} \rightarrow\]

The latter looks to much like a limit.

Answer 12

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."

Answer 13

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.

Answer 14

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

Answer 15

That's a bit of a leap. Try just using the variables I defined. If they all did 71 pushups then:

\[ M + S + B = 71\]

Answer 16

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

Answer 17

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

Answer 18

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

Answer 19

2(m)=s

Answer 20

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
\[ \rightarrow ?\]

Answer 21

im lost

Answer 22

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

Answer 23

m-5=b

Answer 24

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

Answer 25

im so confused

Answer 26

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

Answer 27

ok

Answer 28

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

Answer 29

i think

Answer 30

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

Answer 31

Does that make sense?

Answer 32

not at all

Answer 33

S = 2M

S + 5 = 2M + 5 right?

Answer 34

If S = 2M

then S + SOMETHING = 2M + SOMETHING

Answer 35

That is what equals means

Answer 36

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

Answer 37

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

Answer 38

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.

Answer 39

ok
i understand that

Answer 40

So if we have an equation

M + S + B = 71, we can replace the S with 2M right?

Answer 41

yea

Answer 42

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

Answer 43

M+2(M)=71?

Answer 44

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?

Answer 45

M+2M+M-5

Answer 46

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.

Answer 47

32m 16s 23b

Answer 48

?

Answer 49

thats not right

Answer 50

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

Answer 51

38 19 14

Answer 52

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

Answer 53

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.

Answer 54

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)

Answer 55

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

Answer 56

a+b+c=-48

Answer 57

Perfect. Now the next sentence.

The first number is 12 more than the second.
Therefore?

Answer 58

A=12+B

Answer 59

And finally,

The third number is 20 less than twice the second number.

Answer 60

C=20-2(b)

Answer 61

Not quite.

Answer 62

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.

Answer 63

20-2(b)=C

Answer 64

No.

Answer 65

C = 2B - 20

Answer 66

ok

Answer 67

?

Answer 68

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.

Answer 69

once again im lost

Answer 70

A + B + C = -48
A = 12 + B
So..
? + B + C = -48

Fill in the ?

Answer 71

36

Answer 72

... No

A = 12 + B.
So
(A) + B + C = (12+B) + B + C right??

Answer 73

ya

Answer 74

If A + B + C = -48
and A = 12 + B
and C = 2B - 20

the (A) + B + (C) = ?

Answer 75

Just replace the A and the C.

Answer 76

with what?

Answer 77

With what they equal.

Answer 78

i cant tell you what a equals without knowing b

Answer 79

............... 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.

Answer 80

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

Answer 81

12+b+2b-20

Answer 82

Right. And what does that equal again?

Answer 83

=-48

Answer 84

So what does B equal ?

Answer 85

Actually that's not quite right.

Answer 86

-8

Answer 87

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

Answer 88

Rewrite the equation again.

A + B + C = -48, A = B + 12, C = 2B-20
So...

Answer 89

idk man

Answer 90

im dying here

Answer 91

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

Right?

Answer 92

yea

Answer 93

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

Answer 94

-36

Answer 95

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