A commercial bakery uses flour, sugar, and butter as the main ingredients by weight to pro… — GMAT

A commercial bakery uses flour, sugar, and butter as the main ingredients by weight to produce a specialized pastry mix. Flour accounts for $0.50$ of the total weight of the mix. Sugar accounts for $\frac{3}{8}$ of the remaining weight of the mix. If the rest of the mix consists of $15$ kilograms of butter, what is the total weight, in kilograms, of the pastry mix?

A
$24$
$48$ Cevap
C
$60$
D
$80$
E
$120$

Cevap

The total weight of the pastry mix is

48

kilograms.

The option stating

48

is correct because flour leaves

\frac{1}{2}

of the total mix. Sugar takes

\frac{3}{8}

of that half, leaving

\frac{5}{8}

of the half for butter. Thus, butter accounts for

\frac{5}{16}

of the total mix. Solving

\frac{5}{16} \times W = 15

yields

W = 48

kg.

Adım Adım Çözüm

Determine the fraction of the total weight remaining after accounting for flour.

Since flour represents

0.50 = \frac{1}{2}

of the total weight

W

, the remaining weight is

1 - \frac{1}{2} = \frac{1}{2}W

The base for the sugar component is specified as the remaining weight after flour.

Calculate the fraction of the total weight represented by butter.

Sugar takes

\frac{3}{8}

of the remaining weight, so butter takes the remaining

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

of the remaining weight. Therefore, butter is

\frac{5}{8} \times \frac{1}{2}W = \frac{5}{16}W

Butter forms the rest of the mixture after sugar is accounted for within the remaining weight.

Set up an equation with the given butter weight to solve for total weight

W

\frac{5}{16}W = 15 \implies W = 15 \times \frac{16}{5} = 3 \times 16 = 48$ kg.

Equating the algebraic fractional expression to the known numerical weight yields the overall total.

Anahtar Kavram

Multi-step successive fraction arithmetic with changing base values

Soru

Cevap

Adım Adım Çözüm

Anahtar Kavram

Sık Yapılan Hatalar

Konular

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