Kinda lost

[Obsession]

Use algebraic techniques to answer the following two questions. Be sure to show and explain your work.

The sum of two 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?


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I'm a little confused with this problem. I got as far as setting up one equation, not sure if it'll help me at all, but I tried:
x + y = 68
and then...everything went downhill.

 

[skeeter]

The sum of two numbers is 68.

x + y = 68

If the larger number is divided by the smaller, the quotient is 7 and the remainder is 4. let x be the larger number ...

x/y = 7 + 4/y
or
x = 7y + 4

solve.

 

[Obsession]

Ok, still a little confused,

x = 7y + 4

subtract 4 from both sides,

7y = x - 4

divide both sides by 7

y = 1/7x - 4/7

Then I thought I should plug it into the original equation, x + y = 68. So:
(1/7x - 4/7) + y = 68, but when I try to solve this equation I don't get anything that might even seem like the answer or something that might help.

 

[skeeter]

you're making this way too difficult on yourself ...

x + y = 68

x = 7y + 4

substitute (7y + 4) for x in the first equation ...

(7y + 4) + y = 68

solve for y, then find x.

 

[Obsession]

That works, too...(i feel stupid)

so (7y + 4) + y = 68
subtract 4 from both sides:
7y + y = 64
or
8y = 64
divide by 8
y = 8
x + 8 = 68
x = 60
----
60 / 8 = 7 r4
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thank you so much