Algebra practice question

Answer: D. $19.80

The four parts total the whole price: (1/3)c + (1/4)c + 2.50 + 5.75 = c. Since 1/3 + 1/4 = 7/12, this is (7/12)c + 8.25 = c, so 8.25 = (5/12)c and c = 8.25(12/5) = 19.80. Check: 19.80/3 = 6.60, 19.80/4 = 4.95, and 6.60 + 4.95 + 2.50 + 5.75 = 19.80. (A) $11.55 comes from adding the fractions incorrectly as 1/3 + 1/4 = 2/7, giving (5/7)c = 8.25. (B) $13.80 comes from omitting the $2.50 packaging cost, solving (5/12)c = 5.75. (C) $16.50 comes from treating the books-and-shipping share as 1/2 of the price, solving (1/2)c = 8.25.

Why the other answers are wrong

A. $11.55

You added the fractions by adding numerators and denominators: 1/3 + 1/4 is 7/12, not 2/7. Solving (5/7)c = 8.25 gives $11.55.

B. $13.80

You left out the $2.50 for packaging and solved (5/12)c = 5.75. The fixed costs total $8.25, not $5.75.

C. $16.50

You treated books plus shipping as half the price, but 1/3 + 1/4 = 7/12, so the leftover fraction is 5/12, not 1/2.

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…