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Question 173519This question is from textbook Harcourt Math
: The question is "Two numbers have a sum of 64. The quotient is 7. What are the two numbers?" Please help and maybe explain or try and walk me through the solution of this problem!! Thank you very much in advance!!
This question is from textbook Harcourt Math
Found 2 solutions by stanbon, gonzo:
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! The question is "Two numbers have a sum of 64. The quotient is 7. What are the two numbers?"
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Let the numbers be x and 64-x.
Comment: Notice that they add up to 64.
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Equation:
x/(64-x) = 7
Comment: That follows from "The quotient is 7".
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Solve the equation:
Cross-multiply to get:
x= 7(64-x)
x = 448 - 7x
Add 7x to both sides to get
8x = 448
Divide both sides by 8 to get:
x = 56 (one of the numbers is 56)
64-x = 64-56 = 8 (the other number is 8)
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Cheers,
Stan H.
Answer by gonzo(654) (Show Source):
You can put this solution on YOUR website! let the 2 numbers be a and b
then:
a + b = 64 (sum of the 2 numbers is 64)
also:
a/b = 7 (quotient of one of the numbers divided by the other number is 7)
we picked a to be the numerator and b to be the divisor.
we could have picked b to be the numerator and a to be the divisor.
the choice was ours since it was not specified which of the numbers had to be the numerator.
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you have 2 equations to work with:
a + b = 64
a/b = 7
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solve one of the variables (a and b are variables) in terms of the other.
you can use either equation but it looks like it would be simpler to use the second equation.
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a/b = 7 is the equation we are going to work with and we will solve for a in terms of b.
starting again:
a/b = 7
multiply both sides of the equation by b to get:
a = 7*b
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we go back to the first equation:
a + b = 64
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we substitute 7*b for a to get:
7*b + b = 64
we combine likes together (7*b and 1*b are likes) to get:
8*b = 64
we divided both sides of the equation by 8 to get
b = 64/8 = 8
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we have solved for b.
now we take one of the equations and solve for a.
take the second equation which is:
a/b = 7
since b = 8, this equation becomes:
a/8 = 7
multiply both sides of equation by 8 to get:
a = 7*8 = 56
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we have values for a and b:
a = 56
b = 8
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plug these values into the other equation to see if that equation holds true.
that other equation is:
a + b = 64
substituting 56 for a, and 8 for b, this equation becomes:
56 + 8 = 64
64 = 64
this equation is true.
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since both equations are true with a value of a = 56 and b = 8, these values are good and the problem is solved.
one of the numbers is 56
the other number is 8.
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note that i didn't have to prove a/b = 7 is true because i used it to solve for the second variable and, in doing so, forced it to be true.
i said:
a/8 = 7
then
a = 8*7 = 56
by solving for a, i forced that equation to be true.
to prove that, substitute anyway:
a/b = 7
substitute 56 for a, and 8 for b to get:
56/8 = 7
7=7
equation is true.
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