AlgebraVery hardTwo-variable inequality with a context
Algebra practice question
A bakery has 20 kilograms of flour. A loaf uses 0.5 kilograms and a cake uses 0.8 kilograms. If the bakery makes x loaves and y cakes, which inequality represents the flour constraint?
- A. 0.5x + 0.8y ≤ 20Correct
- B. 0.5x + 0.8y ≥ 20
- C. x + y ≤ 20
- D. 0.8x + 0.5y ≤ 20
Answer: A. 0.5x + 0.8y ≤ 20
Flour used is 0.5 per loaf and 0.8 per cake, and it can't exceed 20.
Why the other answers are wrong
- B. 0.5x + 0.8y ≥ 20
- ≥ would require using at least 20 kg — the flour is a limit, not a minimum.
- C. x + y ≤ 20
- x + y ≤ 20 ignores that loaves and cakes use different amounts.
- D. 0.8x + 0.5y ≤ 20
- Swaps the amounts for loaves and cakes.
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.