SOLUTION: The problem is as follows: " The sum of two integers is ten. Three times the larger integer is three less than eight times the smaller integer. Find the integers. " I need to

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: The problem is as follows: " The sum of two integers is ten. Three times the larger integer is three less than eight times the smaller integer. Find the integers. " I need to       Log On


   

Question 309597: The problem is as follows:
" The sum of two integers is ten. Three times the larger integer is three less than eight times the smaller integer. Find the integers. "
I need to know how to write and solve an equation for this word problem.
Thank you.
Found 2 solutions by Earlsdon, Edwin McCravy:
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Let a = the smaller integer and b = the larger integer, then:
1) a+b = 10 "The sum of two integers is ten." and...
2) 3b = 8a-3 "Three times the larger integer is three less than eight times the smaller integer."
These are the equations you will need to solve this problem.
Rewrite equation 1) as:
1a) b = 10-a and substitute into equation 2) for b.
2a) 3(10-a) = 8a-3 Solve this for a.
30-3a = 8a-3 Add 3a to both sides.
30 = 11a-3 Add 3 to both sides.
33 = 11a Finally, divide both sides by 11.
3 = a or a = 3.
b = 10-a
b = 10-3 = 7
The integers are: 3 and 7.

Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
The problem is as follows:
" The sum of two integers is ten. Three times the larger integer is three less than eight times the smaller integer. Find the integers. "
I need to know how to write and solve an equation for this word problem.
Thank you.

There are two methods depnding on whether you want to 
let the unknown n be the smaller or the larger.

>>...The sum of two integers is ten...<<

This says:

SMALLER + LARGER = 10

Method 1 uses

SMALLER = 10 - LARGER 

with n = larger and 10-n = smaller

Method 2 uses

LARGER = 10 - SMALLER.

with n = smaller and 10-n = larger.

Here's how to do it using method 1:

--------------------------------------

Using method 1, this sentence

Three times the larger integer is three less than eight times the smaller integer.

becomes

Three times n is three less than eight times 10-n.

or

3n is 3 less than 8*(10-n). 

or

3n is 8*(10-n) MINUS 3

or

3n = 8*(10-n) - 3

Solve that and get n = larger = 7, then smaller = 10-n = 10-7 = 3

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Here's how to do it using method 2:

--------------------------------------

Using method 2, this sentence

Three times the larger integer is three less than eight times the smaller integer.

becomes

Three times 10-n is three less than eight times n.

or

3*(10-n) is 3 less than 8*n. 

or

3*(10-n) is 8*n MINUS 3

or

3*(10-n) = 8n - 3

Solve that and get n = amaller = 3, then larger = 10-n = 10-3 = 7

Both ways are equally correct.  Take your pick.
------------------------------------------------------------
Edwin