SOLUTION: One number is four more than three times another number. Find the numbers if the product is 175. What I have tried: 3n(n+4)= 175 3n

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Question 714640: One number is four more than three times another number. Find the numbers if the product is 175.
What I have tried: 3n(n+4)= 175

3n^2+9-175

Found 2 solutions by Alan3354, MathLover1:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
One number is four more than three times another number. Find the numbers if the product is 175.
What I have tried: 3n(n+4)= 175 **** How did you come up with that?
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n = a number
The other number is 4 plus 3 times the 1st number, = 3n+4
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n*(3n+4) = 175
Start from there.

Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

let numbers be x and y
if a number x is four more than three times number y, then we have:
x=3y%2B4....eq. 1
if the product is 175, than we have:
xy=175....eq. 2
now, we need to solve the system:
x=3y%2B4....eq. 1
xy=175....eq. 2
_________________________
start with x=3y%2B4....eq. 1 and substitute x in eq. 2
%283y%2B4%29y=175....eq. 2
3y%5E2%2B4y=175
3y%5E2%2B4y-175=0......use quadratic formula
y=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
y=+%28-4+%2B-+sqrt%28+4%5E2-4%2A3%2A%28-175%29+%29%29%2F%282%2A3%29+
y=+%28-4+%2B-+sqrt%2816%2B2100+%29%29%2F6+
y=+%28-4+%2B-+sqrt%282116+%29%29%2F6+
y=+%28-4+%2B-+46%29%2F6+
solutions:
y=+%28-4+%2B+46%29%2F6+
y=+42%2F6+
highlight%28y=+7%29+
or
y=+%28-4+-46%29%2F6+
y=+-50%2F6+
highlight%28y=-8.3333333333333333333333333333333%29+

now find x

x=3y%2B4....eq. 1...plug in y=7
x=3%2A7%2B4
x=21%2B4
highlight%28x=25%29
or
x=3y%2B4....eq. 1...plug in y=-8.3333333333333333333333333333333
x=3%2A%28-8.3333333333333333333333333333333%29%2B4
x=-25%2B4
highlight%28x=-21%29
so, we have two pairs, one is highlight%28x=25%29 and y=7
and another one is highlight%28x=-21%29 and y=-8.3333333333333333333333333333333
check:
xy=175.....plug in first pair
25%2A7=175
175=175....true
xy=175.....plug in second pair
-21%2A%28-8.3333333333333333333333333333333%29=175
174.99999999999999999999999999999=175....round it to whole number
175=175....true