Let's put this in terms of a system of equations. Let's call the numbers x and y, with x being the larger integer and y the smaller one. Since they are consecutive odd integers, we know that:
x = y + 2
The constraint is:
xy= 3(x+y) + 71 Simplify
xy = 3x + 3y + 71 Plug in (y+2) for x:
(y + 2) y = 3(y + 2) + 3y + 71 Simplify
y² + 2y = 3y + 6 + 3y + 71 Subtract 6y from both sides, add 71+6
y² -4y = 77
y² - 4y - 77 = 0
Factor:
(y - 11) (y+7) = 0
y = 11 or y=-7
When y = 11, x = 13, since x = y+2
Plug in to make sure:
xy = 3(x+y) + 71
11*13 = 3 (11 + 13) + 71
143 = 3 (24) + 71
143 = 72 + 71
143 = 143
Our values work!
Answer: 11, 13
Answer:
Ray = 19 yrs old
Tom = 25 yrs old
John = 57 yrs old
Explanation:
Let x be the years of Tom
R = x - 6
J = 3R = 3(x - 6)
T = x
R + J + T = 101
x - 6 + 3(x - 6) + x = 101
2x - 6 + 3x - 18 = 101
5x - 24 = 101
5x = 125
x = 125/5 = 25
R = 25 - 6 = 19
J = 3(25 - 6) = 57
T = 25
Sure but where is the test?
The formula for the area of a triangle is (1/2)bh = A
when we plug in the numbers, we get (1/2)(3x-1)x = A
using the distributive property we get (1.5x - .5)x = A
Then its 1.5x^2 - .5x = A
then if we factor out 0.5x we get 0.5x(3x-1) = A
then with the zero product property, 0.5x can equal 0 and x would need to equal 0.
if 3x-1 = 0 , then 3x = 1 then x = 1/3. so our answer would be 1/3 I'm pretty sure because a length cannot be 0
