SOLUTION: I'm desperately trying to help my 8th grade daughter with this, & my 45-year-old math skills are lacking. Hope you can help. Use algebraic techniqies to solve the problem: The

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Question 169043: I'm desperately trying to help my 8th grade daughter with this, & my 45-year-old math skills are lacking. Hope you can help.
Use algebraic techniqies to solve the problem:
The sum of 2 numbers is 68. If the larger number is divided by the smaller, the quotient is 7 and the remainder is 4. What is the larger number?
Thanks, in advance.
Found 3 solutions by Earlsdon, Alan3354, ptaylor:
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Try this:
Let a be the larger number and b the smaller number.
From the problem description, you have:
1) a%2Bb+=+68 "The sum of the two numbers is 68." and ...
2) a%2Fb+=+7+4%2Fb "If the larger number is divided by the smaller number, the quotient is 7 with a remainder of 4"
Rewrite equation 2) as:
a+=+7b%2B4 and substitute this into equation 1)
%287b%2B4%29%2Bb+=+68 Simplify.
8b%2B4+=+68 Subtract 4 from both sides.
8b+=+64 Divide both sides by 8.
b+=+8 and
a+=+7b%2B4
a+=+7%288%29%2B4
a+=+56%2B4
a+=+60 The larger number is 60 and the smaller number is 8.
Check:
a%2Bb+=+60%2B8=68 Ok!
a%2Fb+=+60%2F8=7%2B4%2F8 or 7 + remainder of 4

Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
The sum of 2 numbers is 68. If the larger number is divided by the smaller, the quotient is 7 and the remainder is 4. What is the larger number?
Thanks, in advance.
-----------------
b = big number
s = small number
b+s = 68
b/s = 7 with rem 4 means that 7*s + 4 = b
b = 7s+4
Substitute for b in the 1 equation
b+s = 68
7s+4 + s = 68
8s + 4 = 68
8s = 64
s = 8, so
b = 60 That's what was asked for.

Answer by ptaylor(2198) About Me  (Show Source):
You can put this solution on YOUR website!
Let x=larger number
And y=the smaller number
Now we are told the following:
x+y=68-------------------------------eq1
x/y=7+4/y multiply each term by y
x=7y+4 ------------------------------------eq2
Substitute eq2 into eq1 and we get:
7y+4+y=68 subtract 4 from each side
8y=68-4=64 divide each side by 8
y=8-----------------------------the smaller number
Substitute y=8 into eq1:
8+y=68 subtract 8 from each side:
y=60------------------------larger number
CK
60/8=7 with a remainder of 4 or 7+4/8=7 1/2

Hope this helps----ptaylor