At a local bookstore, 40\% of the total inventory consists of fiction books. Of the remain… — ACT

At a local bookstore, $40\%$ of the total inventory consists of fiction books. Of the remaining inventory, $\frac{5}{8}$ consists of non-fiction books, and the rest are children's books. If there are $270$ children's books in the bookstore, what is the total number of books in the inventory?

A
$450$
B
$675$
C
$720$
$1,200$ Cevap
E
$1,800$

Cevap

1,200

Fiction books account for

40\%

of the total inventory, leaving

60\%

as the remaining portion. Since

\frac{5}{8}

of this remainder is non-fiction, the children's books represent the other

\frac{3}{8}

of that

60\%

remainder. Multiplying

\frac{3}{8} \times 0.60 = 0.225

, or

22.5\%

of the total inventory. Given that there are

270

children's books, dividing

270

0.225

yields the total inventory of

1,200

books.

Adım Adım Çözüm

Determine the fraction of inventory remaining after accounting for fiction books.

Remaining fraction =

100\% - 40\% = 60\% = 0.6 = \frac{3}{5}

Fiction accounts for

40\%

, leaving

60\%

of the total inventory for other genres.

Find the fraction of the remaining inventory that consists of children's books.

Children's fraction of remaining =

1 - \frac{5}{8} = \frac{3}{8}

Since

\frac{5}{8}

of the remaining inventory is non-fiction, the rest (

\frac{3}{8}

) must be children's books.

Calculate the proportion of the total inventory that children's books represent.

Children's proportion of total =

\frac{3}{8} \times \frac{3}{5} = \frac{9}{40} = 0.225 = 22.5\%

Multiply the fraction of the remainder by the fraction of the total remaining.

Set up an equation with total inventory

T

and solve for

T

0.225 \times T = 270 \implies T = \frac{270}{0.225} = 1,200

Divide the known count of children's books (

270

) by its fractional share of the total inventory.

Anahtar Kavram

Solving multi-step word problems involving fractions, decimals, and percentages of a whole

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