*Use a quadratic equation to solve :
1. the larger of two numbers is 5 more than the smaller. The product of the numbers is 204. Find the numbers.
2 . find two positive numbers in the ratio 2:3 whose product is 2400.

Question

*Use a quadratic equation to solve :
1. the larger of two numbers is 5 more than the smaller. The product of the numbers is 204. Find the numbers.
2 . find two positive numbers in the ratio 2:3 whose product is 2400.

pfenn1 · Answer

If x is the larger number and y is the smaller number, what would be the equation for "the larger of two numbers is 5 more than the smaller"?

pfenn1 · Answer

How about "the product of the numbers is 204"?

anonymous · Answer

idk that's why i am asking, i am confused with this!

pfenn1 · Answer

If x (the larger of two numbers) is 5 more than y (the smaller), how would write that in an equation?

anonymous · Answer

x>5y ?

pfenn1 · Answer

Close, what you wrote could be written as the larger number is greater than 5 times the smaller number.
x (the larger of two numbers) is 5 more than y (the smaller)
x                                            =  5      +         y

anonymous · Answer

so it's x=5+y ?

pfenn1 · Answer

Yes.  A lot of what you are trying to do in "word problems" is to try to develop the equations that underlie the sentences.  Do you know which mathematical function is implied by the "product"?

anonymous · Answer

multiplyinng?

pfenn1 · Answer

Correct. so what would "the product of the numbers is 204" imply?

anonymous · Answer

204=x? 
(5+y) * y = 204?

pfenn1 · Answer

Yes.  The first equality 204=x? should be 204=xy but the second is correct.
(5+y) * y = 204
So now rearrange and solve for y.  And then use x=5+y to solve for x.

anonymous · Answer

what about the second one can you help me with it?

anonymous · Answer

y= -17 or 12

pfenn1 · Answer

Sure. If x and y are two positive numbers, then "two numbers in the ratio 2:3" I think implies that $$\left( x \over y \right) = \left( 2 \over 3 \right)$$
The second equation is based on the "product" of the two numbers is 2400.  Can you write that second equation?

pfenn1 · Answer

Yes, I got the same solution to question 1. y=-17 or 12

anonymous · Answer

$$\left(\begin{matrix}2 \ 3\end{matrix}\right) = \left(\begin{matrix}2400 \ x\end{matrix}\right)$$    which means x= 3600?

pfenn1 · Answer

I'm not sure what you did there...
The "product" of the two numbers is 2400 implies $$xy=2400$$If you rearrange the first equation, $$\left( x \over y \right) = \left( 2 \over 3 \right)$$To solve for x you get$$x = \left( 2y \over 3 \right)$$Plug that into
$$xy=2400$$and solve for y

anonymous · Answer

so it is 3600

pfenn1 · Answer

No, that isn't what I got. 
$$\left( 2y ^{2}\over 3 \right)=2400$$rearrange to get$$y ^{2}=2400 \left( 3 \over 2 \right)=3600$$

pfenn1 · Answer

3600 can't be the right answer because 3600x=2400 would imply that x is <<<3600 and the ratio of x/y = 2/3.  Sometimes you can check your answers by just seeing if they make any sense.

pigrenex · Answer

try to solve it by these two equations $$x \div y=2\div3$$ and $$x \times y =2400$$ rearrange the equation 2, isolating y. finally, insert it in the equation 1