A high school athletic department set a total fundraising goal of \2,400 for new equipment… — ACT

A high school athletic department set a total fundraising goal of $\$2,400$ for new equipment. During the first week, the department raised $\frac{3}{8}$ of the total goal. During the second week, they raised $35\%$ of the total goal. During the third week, they raised $0.15$ of the total goal. How much money must the department raise in the fourth week to meet its total goal exactly?

A
$\$288$
$\$300$ Answer
C
$\$480$
D
$\$615$
E
$\$2,100$

Answer

The athletic department must raise

\$\text{300}

in the fourth week to meet its total goal.

Converting each portion into a dollar value relative to the total goal of

\$\text{2,400}

gives

\$\text{900}

for the first week,

\$\text{840}

for the second week, and

\$\text{360}

for the third week. Adding these amounts yields

\$\text{2,100}

raised in total. Subtracting

\$\text{2,100}

from

\$\text{2,400}

gives the remaining requirement of

\$\text{300}

Step-by-Step Solution

Calculate the amount raised in Week 1 using the fraction

\frac{3}{8}

\frac{3}{8} \times \$2,400 = \$900

To find a fractional part of a total amount, multiply the total by the fraction.

Calculate the amount raised in Week 2 using the percentage

35\%

0.35 \times \$2,400 = \$840

Convert

35\%

to a decimal (

0.35

) and multiply by the total goal.

Calculate the amount raised in Week 3 using the decimal

0.15

0.15 \times \$2,400 = \$360

Multiply the decimal fraction directly by the total goal.

Sum the amounts raised during the first three weeks and subtract from the total goal.

Total raised =

\$900 + \$840 + \$360 = \$2,100

; Remaining needed =

\$2,400 - \$2,100 = \$300

Subtracting the total funds collected so far from the target yields the remaining requirement.

Key Concept

Fractions, Decimals, and Percentages

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