Carcass wrote:
If \(\frac{x}{y}=\frac{2}{3}\) and x + y = 15 , which of the following is greater than y ?
Indicate all possible choices.
A. \(\sqrt{65}\)
B. \(\sqrt{82}\)
C. \(\sqrt{99}\)
D. \(\sqrt{101}\)
E. \(\sqrt{122}\)
GIVEN: x/y = 2/3
Cross multiply to get:
3x = 2yAlso given:
x + y = 15If
x + y = 15, then we can write: x = 15 - y
Now take
3x = 2y and replace x with 15 - y
We get: 3(15 - y) = 2y
Expand: 45 - 3y = 2y
Add 3y to both sides: 45 = 5y
Solve:
y = 9Which of the following is greater than y ? In other words,
which of the following is greater than 9?ASIDE:
√64 = 8
√81 = 9
√100 = 10
√121 = 11
√144 = 12
Since √81 = 9, we're looking for all answer choices that are GREATER THAN √81
Answer: B, C, D, E