AlgebraVery hardChoosing a system that models a situation
Algebra practice question
A gardener buys x bags of compost at $6 each and y bags of bark at $9 each, spending $105 in total. She buys twice as many bags of compost as bags of bark. Which system of equations represents this situation?
- A. 6x + 9y = 105 and x = 2yCorrect
- B. 6x + 9y = 105 and y = 2x
- C. 9x + 6y = 105 and x = 2y
- D. 6x + 9y = 105 and x + y = 2
Answer: A. 6x + 9y = 105 and x = 2y
Cost: 6x + 9y = 105. Twice as many compost bags as bark bags: x = 2y. (The solution is y = 5, x = 10: 60 + 45 = 105.)
Why the other answers are wrong
- B. 6x + 9y = 105 and y = 2x
- y = 2x says twice as much bark as compost, the reverse.
- C. 9x + 6y = 105 and x = 2y
- Swaps the prices.
- D. 6x + 9y = 105 and x + y = 2
- x + y = 2 says two bags in total, which the $105 rules out.
More Algebra questions
- Very hard
For what value of c does the system 3x − 2y = 8 and 9x + cy = 5 have no solution? - Very hard
In the system 5x + 4y = 32 and 3x − 2y = 6, what is the value of 8x + 2y? - Very hard
The solution set of the inequality |ax − b| ≤ 6, where a and b are constants and a > 0, is 3 ≤ x ≤ 9. What is … - Very hard
The function f is linear, and for every value of x, f(x + 2) − f(x) = 6. If f(5) = 4, what is the value of f(0… - Very hard
In the system of equations 2x + 3y = 12 and 5x − 2y = k, where k is a constant, the solution (x, y) satisfies … - Very hard
In the xy-plane, the system of equations kx + 6y = 12 and 2x + (k − 1)y = 6, where k is a constant, has infini…
Not affiliated with the College Board. SAT is a trademark of the College Board.