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Question 992791: Im dying kindly help me please . One number exceeds another by 7 if the larger number is increase by 4 it will be equal to 1 less than 4 times the smaller number decreased by 6 find tbe origibal number.
-please help...
Found 2 solutions by ikleyn, Theo:
Answer by ikleyn(52803)   (Show Source):
You can put this solution on YOUR website! .
One number exceeds another by 7. If the larger number is increased by 4 it will be equal to 1 less than 4 times the smaller number decreased by 6. Find the original number.
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1. Your writing was not perfect. It was difficult to read and to understand it. I edited and fixed it.
2. Let x be the larger number. Then the other number is (x-7).
" If the larger number is increased by 4" -----> x + 4
"4 times the smaller number decreased by 6" -----> 4*((x-7)-6)
The equation is
x + 4 = 4*((x-7)-6) - 1.
Simplify and solve it:
x + 4 = 4*(x-13) - 1,
x + 4 = 4x - 52 - 1,
3x = 4 + 52 + 1 = 57,
x =  = 19.
Answer by Theo(13342)  (Show Source):
You can put this solution on YOUR website! x is the larger number
y is the smaller number.
one number exceeds the other number by 7.
x = y + 7
if the larger number is increased by 4, it will be equal to 1 less than 4 times the smaller number decreased by 6.
x + 4 = 4 * y - 6
or:
x + 4 = 4 * (y - 6)
not sure which.
find the original numbers.
first option, you have:
x = y + 7
x + 4 = 4 * y - 6
start with:
x = y + 7
x + 4 = 4 * y - 6
replace x in the second equation with y + 7 from the first equation to get:
y + 7 + 4 = 4 * y - 6
combine like terms to get:
y + 11 = 4 * y - 6
subtract y from both sides of the equation and add 6 to both sides of the equation to get:
17 = 3 * y
solve for y to get y = 17/3.
second option, start with:
x = y + 7
x + 4 = 4 * (y - 6)
replace x in the second equation with y + 7 from the first equation to get:
y + 7 + 4 = 4 * (y - 6)
combine like terms on the left side of the equation and simplify the right side of the equation to get:
y + 11 = 4 * y - 24
subtract y from both sides of the equation and add 24 to both sides of the equation to get:
35 = 3 * y
solve for y to get y = 35/3.
it's really hard to tell what is meant by the problem statement.
is it (4 * the smaller number), decreased by 6, or is it 4 times (the smaller number decreased by 6).
in real world cases like this, you usually ask the person which one they meant, but since this is algebra, you can't do that, and you're left guessing.
a reference on keywords can be found here:
sometime they're helpful.
http://www.purplemath.com/modules/translat.htm
if i had to choose, i would pick the second interpretation.
that would be:
4 times (the smaller number decreased by 6).
but it could easily be the other as well.
50/50 whether you get it right or not.
once you decide what the right interpretation is, you then solve it using the rules of algebraic operations.
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