anonymous
  • anonymous
Three-fourths of seven less than a number is forty-two. Find the number.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
my ans is -147/4
anonymous
  • anonymous
(3/4)(x-7) = 42. Gogogo
anonymous
  • anonymous
\[\frac{3(x-7)}{4} = 42 \rightarrow \frac{4(42)}{3} = x-7 \rightarrow x=?\]

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anonymous
  • anonymous
so the number is 49?
anonymous
  • anonymous
Close.. \[ x-7 = 56 \rightarrow x-7+7 = 56 +7 = x = ?\]
anonymous
  • anonymous
63?
anonymous
  • anonymous
Indeed.
anonymous
  • anonymous
ok i got another for you...i like your help
anonymous
  • 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
  • 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
  • anonymous
\[\text{Polpak I prefer } \implies\ \text{instead of} \rightarrow\] The latter looks to much like a limit.
anonymous
  • 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
  • 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
  • anonymous
\[2s +m=5-m=71 ?\]
anonymous
  • 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
  • anonymous
Then we look at how M, S, and B are otherwise related.
anonymous
  • anonymous
"Bonnie did 5 less pushups then Mark" \[ \rightarrow B = M-5\]
anonymous
  • anonymous
"Suzzette did twice as many pushups as mark" \[ \rightarrow ?\]
anonymous
  • anonymous
2(m)=s
anonymous
  • 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
  • anonymous
im lost
anonymous
  • anonymous
I plugged in 2M for S in the M + S + B = 71 equation. Now do the same for B.
anonymous
  • anonymous
m-5=b
anonymous
  • anonymous
Yes, that's the equation for what B _is_. Now use that in the equation M + S + B = 71
anonymous
  • anonymous
im so confused
anonymous
  • anonymous
B = M - 5. Would you agree then that M + S + B = M + S + (M-5) ?
anonymous
  • anonymous
ok
anonymous
  • anonymous
And since S = 2M Would you agree that M + S + (M-5) = M + 2M + M - 5 ?
anonymous
  • anonymous
i think
anonymous
  • 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
  • anonymous
Does that make sense?
anonymous
  • anonymous
not at all
anonymous
  • anonymous
S = 2M S + 5 = 2M + 5 right?
anonymous
  • anonymous
If S = 2M then S + SOMETHING = 2M + SOMETHING
anonymous
  • anonymous
That is what equals means
anonymous
  • anonymous
I don't understand what you're not understanding. Which part is confusing?
anonymous
  • anonymous
im a retard when it comes to math...i dnt even know where to begin to solve ur problem
anonymous
  • 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
  • anonymous
ok i understand that
anonymous
  • anonymous
So if we have an equation M + S + B = 71, we can replace the S with 2M right?
anonymous
  • anonymous
yea
anonymous
  • anonymous
So rewrite the equation by replacing the S. Also replace the B since we know that B = M-5.
anonymous
  • anonymous
M+2(M)=71?
anonymous
  • 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
  • anonymous
M+2M+M-5
anonymous
  • 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
  • anonymous
32m 16s 23b
anonymous
  • anonymous
?
anonymous
  • anonymous
thats not right
anonymous
  • anonymous
\[ M + 2M + M -5 = 71\] \[ \rightarrow 4M -5 = 71 \] \[ \rightarrow 4M = 76 \] \[ \rightarrow M = 76/4 \] \[ \rightarrow M = 19 \]
anonymous
  • anonymous
38 19 14
anonymous
  • anonymous
S = 2M = 2(19) = 38 B = M-5 = 19-5 = 14
anonymous
  • 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
  • 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
  • anonymous
The first sentance is: The sum of the three numbers is -48. So your equation is ?
anonymous
  • anonymous
a+b+c=-48
anonymous
  • anonymous
Perfect. Now the next sentence. The first number is 12 more than the second. Therefore?
anonymous
  • anonymous
A=12+B
anonymous
  • anonymous
And finally, The third number is 20 less than twice the second number.
anonymous
  • anonymous
C=20-2(b)
anonymous
  • anonymous
Not quite.
anonymous
  • 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
  • anonymous
20-2(b)=C
anonymous
  • anonymous
No.
anonymous
  • anonymous
C = 2B - 20
anonymous
  • anonymous
ok
anonymous
  • anonymous
?
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
  • anonymous
once again im lost
anonymous
  • anonymous
A + B + C = -48 A = 12 + B So.. ? + B + C = -48 Fill in the ?
anonymous
  • anonymous
36
anonymous
  • anonymous
... No A = 12 + B. So (A) + B + C = (12+B) + B + C right??
anonymous
  • anonymous
ya
anonymous
  • anonymous
If A + B + C = -48 and A = 12 + B and C = 2B - 20 the (A) + B + (C) = ?
anonymous
  • anonymous
Just replace the A and the C.
anonymous
  • anonymous
with what?
anonymous
  • anonymous
With what they equal.
anonymous
  • anonymous
i cant tell you what a equals without knowing b
anonymous
  • 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
  • anonymous
So put 12 + B where there is an A. And put 2B-20 where there is a C.
anonymous
  • anonymous
12+b+2b-20
anonymous
  • anonymous
Right. And what does that equal again?
anonymous
  • anonymous
=-48
anonymous
  • anonymous
So what does B equal ?
anonymous
  • anonymous
Actually that's not quite right.
anonymous
  • anonymous
-8
anonymous
  • 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
  • anonymous
Rewrite the equation again. A + B + C = -48, A = B + 12, C = 2B-20 So...
anonymous
  • anonymous
idk man
anonymous
  • anonymous
im dying here
anonymous
  • anonymous
A + B + C = (12+B) + B + (2B-20) ^A + ^B + ^C Right?
anonymous
  • anonymous
yea
anonymous
  • anonymous
So if A + B + C = -48, what is B.
anonymous
  • anonymous
-36
anonymous
  • 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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