# Math

Three numbers X, Y, and Z are in the ratio 2:7:8. If 12 is subtracted from Y, then three numbers form a geometric sequence (in the order X, Y–12, Z). Find X, Y, and Z.

There are two sets of answers I already found one set i am unsure how to find the other one.

x=10,y=20,z=80

1. 👍
2. 👎
3. 👁
1. let the 3 numbers be 2x, 7x and 8x
then (7x-12)/(2x) = 8x/(7x-12)

If 2x, (7x-12) and 8x form a GP, then
(7x-12)^2 = 2x(8x)
49x^2 - 168x + 144 = 16x^2
33x^2 - 168x + 144 = 0
11x^2 - 56x + 48 = 0
(x - 4)(11x - 12) = 0
so x = 4 or x = 12/11

if x = 4, the original numbers are 8, 28, and 32
check: subtract 12 from 28 to get new numbers of 8, 16 and 32, which do form a GP

if x = 12/11, then the 3 originals are 24/11, 84/11 and 96/11
take 12 away from 84/11 to get -48/11
check:
-48/11 ÷ 24/11 = -2
96/11 ÷ -48/11 = -2

1. 👍
2. 👎
👤
Reiny
2. What’s the answer?

1. 👍
2. 👎

## Similar Questions

1. ### algebra

Are the following true or false? 1. The difference of two natural numbers is always a natural number. 2. The sum of two natural numbers is always a natural number. 3. The quotient of two natural numbers is always a natural number.

2. ### math

find each sum or difference 1. -1/2 + 1/3 1. -1/6 2. -1/3 3. 2/3 4. 1/6 I got 2/3 because I added the 2 numerators and got 2 then I kept the LCM as the denominator so I got 2/3. 2. -3 1/5 + -6 1/2 1. -3 2/7 2. -3 7/10 3. -9 2/7 4.

3. ### high school (math)

Match the mathematical expression with its translation. 1. the product of two numbers 2. y divided by x 3. six less than a number is y 4. x subtracted from y 5. the sum of two numbers is six 6. x minus y 7. the sum of x and y 8. x

4. ### Art

why did artist such as leonardo da vinci use the golden ratio in their paintings? The enjoyed working with numbers It creates a balanced and intriguing visual composition The like to obey the rigid structure of the ratio Using

1. ### Math

The sum of two numbers subtracted from twice the sum of those numbers. Please help?

2. ### Physics (optics)

A ray of light traveling in air strikes the midpoint of one face of an equiangular glass prism (n = 1.74) at an angle of exactly 30.0â—¦ Trace the path of the light ray through the glass and find the angle of incidence of the

3. ### maths

Two consecutive odd numbers are such that seven times the smaller ,subtracted from nine times the bigger ,144.find two numbers.

4. ### math

the difference between 2 numbers is 40? they are in the ratio 9:7. What are the numbers ?

1. ### Math

Three numbers form a geometric progression. If 4 is subtracted from the third term, then the three numbers will form an arithmetic progression. If, after this, 1 is subtracted from the second and third terms of the progression,

2. ### Algerba II

Hi Do decimals such as 2.718 represent rational numbers or irrational numbers. Explain. Do repeating decimals such as 2.3333 . . . represent rational numbers or irrational numbers? Explain. So I look back in my textbook and find

3. ### Computer Science - MATLAB

One interesting property of a Fibonacci sequence is that the ratio of the values of adjacent members of the sequence approach a number called “the golden ratio” or PHI. Create a program that accepts the first two numbers of a

4. ### Maths

Two numbers are in the ratio 2:7.if sum of the numbers is 99 , find them