word problem of sum of the number

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word problem of sum of the number

Postby Galaxy » Tue 12 April, 2011 18:28

One number is ten more than twice another. If their sum is decreased by nine, the result is sixteen. Find the numbers.
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Re: word problem of sum of the number

Postby barnamah » Tue 12 April, 2011 18:44

it says:
One number is ten more than twice another.
let that one number be x and the another be y
x=10+2y (call this EQ1)

If their sum is decreased by nine, the result is sixteen
16=x+y-9
`16=x+y-9` add 9 to both side we have:
16+9=x+y
25=x+y (call this EQ2)

so we have two unknown and 2 equations. We can solve for x and y
using EQ2 let's solve for x

25=x+y now subtract y from both side we have:
25-y=x

so we got x. Now using EQ1 we can substitute the x
`25-y=10+2y`

bring the terms with y to one side by adding +y to both side:
`25-y+y=10+2y+y`
`25=10+2y+y` collect the like term with y on the right
`25=10+3y`


Now to bring 10 to the left subtract -10 from both side:
`25-10=3y`
`15=3y`
Divide both side by 3
`15/3=(3y)/3`
5=y
so we found y=5
subbing y into EQ2
25=x+y
`25=x+5`
subtract 5 from both side `25-5=x+5-5` and we have:
`20=x`
so x=20

We can test them by putting the values in our EQ1 and EQ2:
in EQ1
x=10+2y
20=10+2(5)
20=20 ✓

in EQ2
25=x+y
25=20+5
25=25 ✓

`:.` The two numbers are 5 and 20.
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