8

Set 16: Linear Equations (Advanced)

Explanation

Answer: C

The sum of two numbers is 20. Twice the first plus the second is 30. What are the numbers?

A.

5, 15

B.

8, 12

C.

10, 10

✓ Correct
D.

6, 14

Detailed Explanation

Choice C is correct. Choice C is the correct answer. 1. Equations: x+y=20x + y = 20, 2x+y=302x + y = 30 2. Subtract 1 st from 2 nd: (2x+y)(x+y)=3020x=10(2 x + y) - (x + y) = 30 - 20 \rightarrow x = 10 3. Find y: 10+y=20y=1010+ y = 20 \rightarrow y = 10 Choice D is incorrect because 2(5)+15=25302(5)+15=25 \neq 30. Choice B is incorrect because 2(8)+12=28302(8)+12=28 \neq 30. Choice C is incorrect because 2(6)+14=26302(6)+14=26 \neq 30.

Key Steps:

The correct answer is 10, 10

Why others are wrong:
A: Choice A is incorrect and may result from a calculation error.
B: Choice B is incorrect and may result from a calculation error.
D: Choice D is incorrect and may result from a calculation error.

🎯 Keep Practicing!

Master all sections for your best SAT score