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Literal Equations and Formulas practice questions

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  1. The volume of a box is V = lwh (length times width times height). Solve for h.

    Answer: h = V ÷ (lw). lwh means l × w × h, so h is multiplied by lw. Divide both sides by lw (assume l and w are not 0): h = V ÷ (lw). Check: a 6 by 5 by 3 box has V = 90, and 90 ÷ (6 × 5) = 3.

  2. Simple interest is I = Prt, where I is the interest in dollars, P is the starting amount, r is the yearly rate as a decimal, and t is the time in years. Solve for r.

    Answer: r = I ÷ (Pt). Prt means P × r × t. Divide both sides by Pt (assume P and t are not 0): r = I ÷ (Pt). Check: 80 dollars of interest on 500 dollars over 2 years gives r = 80 ÷ 1000 = 0.08, which is 8 percent.

  3. Solve 4x + 3y = 24 for y.

    Answer: y = (24 − 4x) ÷ 3. Subtract 4x from both sides: 3y = 24 − 4x. Then divide the whole right side by 3: y = (24 − 4x) ÷ 3. Check with x = 3: y = 12 ÷ 3 = 4, and 4(3) + 3(4) = 24.

  4. The area of a triangle is A = (1/2)bh. Solve for b.

    Answer: b = 2A ÷ h. Multiply both sides by 2 to clear the fraction: 2A = bh. Then divide both sides by h (assume h ≠ 0): b = 2A ÷ h. Check: a triangle with area 30 and height 6 has b = 60 ÷ 6 = 10, and (1/2)(10)(6) = 30.

  5. A rectangular garden has a perimeter of 46 feet and a width of 8 feet. Use P = 2l + 2w to find its length.

    Answer: 15 feet. Substitute: 46 = 2l + 2(8), so 46 = 2l + 16. Subtract 16 to get 2l = 30, then divide by 2 to get l = 15 feet. Check: 2(15) + 2(8) = 46.

  6. The volume of a cone is V = (1/3)πr2h. Solve for h.

    Answer: h = 3V ÷ (πr2). Multiply both sides by 3 to clear the fraction: 3V = πr2h. Now h is multiplied by πr2, so divide both sides by the whole πr2 (assume r ≠ 0): h = 3V ÷ (πr2). Check: a cone with r = 3 and h = 4 has V = 12π, and 3(12π) ÷ (π × 9) = 4.

  7. Solve 4x + n = 7x − 9 for x.

    Answer: x = (n + 9) ÷ 3. Get the x terms together by subtracting 4x from both sides: n = 3x − 9. Add 9 to both sides: n + 9 = 3x. Divide the whole side by 3: x = (n + 9) ÷ 3. Check with n = 6: x = 5, and 4(5) + 6 = 26 = 7(5) − 9.

  8. Jo solved y = 2x + 7 for x and wrote x = y ÷ 2 − 7. What went wrong?

    Answer: She divided y by 2 but not the 7. She should subtract 7 first, then divide the whole side by 2.. The correct steps are: subtract 7 from both sides, then divide the whole side by 2, so x = (y − 7) ÷ 2. Jo divided only y by 2 and left the 7 alone. Check with y = 15: the correct formula gives (15 − 7) ÷ 2 = 4, and 2(4) + 7 = 15. Jo’s formula gives 15 ÷ 2 − 7 = 0.5.

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