16Hit1600
AlgebraHardBuild a linear equation from fractional parts of a total

Algebra practice question

A museum exhibit on textiles displays its entire collection across three galleries. Exactly 3/8 of the textiles are displayed in the first gallery and exactly 1/6 of the textiles are displayed in the second gallery. The remaining 55 textiles are displayed in the third gallery.

How many textiles are in the entire collection?

Answer: 120

Let T be the total number of textiles. Then T - (3/8)T - (1/6)T = 55. Using a common denominator of 24, (24/24)T - (9/24)T - (4/24)T = (11/24)T, so (11/24)T = 55 and T = 55 * (24/11) = 120. Check: (3/8)(120) = 45, (1/6)(120) = 20, and 120 - 45 - 20 = 55. A student who adds the fractions by adding numerators and denominators (3/8 + 1/6 = 4/14 = 2/7) gets (5/7)T = 55 and the incorrect answer 77; a student who overlooks the second gallery gets (5/8)T = 55 and the incorrect answer 88; a student who treats 55 as the fraction 11/24 of T times 11/24 rather than dividing gets about 25.

Common wrong answers

If you answered 25
You multiplied 55 by 11/24 instead of dividing; since (11/24)T = 55, you need T = 55 × 24/11 = 120.
If you answered 55
That's the number in the third gallery, which the question gives you; you need the total collection size T.
If you answered 77
You added the fractions by adding numerators and denominators (3/8 + 1/6 = 4/14 = 2/7), leaving 5/7 of the total; with a common denominator of 24, 3/8 + 1/6 = 13/24, so 11/24 of the total is 55.
If you answered 88
You only subtracted the first gallery's 3/8, giving (5/8)T = 55; you also need to remove the 1/6 in the second gallery, leaving 11/24 of the total.

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