SOLUTION: I have two questions, the 1st one is: #1. The product of two numbers is 10 less than 16 times the smaller. if twice the smaller is 5 more than the larger number, find the two nu

Question 406668: I have two questions, the 1st one is:
#1. The product of two numbers is 10 less than 16 times the smaller. if twice the smaller is 5 more than the larger number, find the two numbers.
I'm having trouble with the first one. The second problem is this:
#2. The area of a rectangular field is 162 sq. m. and its length is twice its width. Find the dimensions of the field.
In number 2 I did this:
Let x = width
2x = length
(2x)(x) = 162
> 2x^2 = 162
> 2x^2/2 = 162/2
> x^2 = 81
> x = 9
I just wanna ask if my answer is correct or do I have to continue and it like this:
> 2x
> 2(9)
> = 18
Looking forward for your response.
Answer by nerdybill(7384) (Show Source): You can put this solution on YOUR website!
#1. The product of two numbers is 10 less than 16 times the smaller. if twice the smaller is 5 more than the larger number, find the two numbers.
.
Let x = smaller of two numbers
and y = larger of two numbers
.
from: "The product of two numbers is 10 less than 16 times the smaller" we get:
xy = 16x-10 (equation 1)
from: "twice the smaller is 5 more than the larger number" we get:
2x = y+5 (equation 2)
.
Solving equation 1 for y:
xy = 16x-10
y = (16x-10)/x
Plug above into equation 2 and solve for x:
2x = y+5
2x = (16x-10)/x+5
multiplying both sides by x:
2x^2 = (16x-10)+5x
2x^2 = 21x-10
2x^2 - 21x + 10 = 0
(2x-1)(x-10) = 0
x = {1/2, 10}
throw out the 1/2 leaving:
x = 10
.
to find y, plug above into:
xy = 16x-10
10y = 160-10
10y = 150
y = 15
.
solution: the two numbers are 10 and 15
.
#2. The area of a rectangular field is 162 sq. m. and its length is twice its width. Find the dimensions of the field.
In number 2 I did this:
Let x = width
2x = length
(2x)(x) = 162
> 2x^2 = 162
> 2x^2/2 = 162/2
> x^2 = 81
> x = 9
I just wanna ask if my answer is correct or do I have to continue and it like this:
> 2x
> 2(9)
> = 18
Yes, you must -- because the problem is asking for "the dimensions".
x gives you only the width
you need to find the length also
complete answer would be 9 meters by 18 meters
(don't forget your units)

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