A non-profit foundation distributes a total grant of \108,000 among three research teams: … — GRE General Test

A non-profit foundation distributes a total grant of $\$108,000$ among three research teams: Team A, Team B, and Team C. Team B receives $\$4,000$ more than Team A. Team C receives twice as much as the combined amount received by Team A and Team B. What amount does Team B receive?

A
$\$16,000$
$\$20,000$ Answer
C
$\$24,000$
D
$\$28,000$
E
$\$72,000$

Answer

Team B receives

\$20,000

Defining Team A's share as

x

gives Team B a share of

x + 4,000

and Team C a share of

2(x + x + 4,000) = 4x + 8,000

. Combining these yields

6x + 12,000 = 108,000

, which solves to

x = 16,000

. Therefore, Team B receives

16,000 + 4,000 = \$20,000

Step-by-Step Solution

Define variables for each team's share in terms of a single unknown variable.

Let

x

be the amount received by Team A in dollars. Then Team B receives

x + 4,000

, and Team C receives

2 \cdot [x + (x + 4,000)] = 2(2x + 4,000) = 4x + 8,000

Expressing all quantities in terms of

x

reduces the problem to a linear equation in one variable.

Set up the linear equation representing the total grant amount.

x + (x + 4,000) + (4x + 8,000) = 108,000 \implies 6x + 12,000 = 108,000

The sum of the individual shares must equal the total grant of

\$108,000

Solve the linear equation for

x

6x = 96,000 \implies x = 16,000

Subtract

12,000

from both sides and divide by

6

Calculate Team B's share using the value of

x

Team B's share

= x + 4,000 = 16,000 + 4,000 = 20,000

The question specifically asks for Team B's share, not Team A's.

Key Concept

Formulating and solving a linear equation in one variable from a multi-step algebraic word problem.

Estimated Time:1m 30s

Question

Answer

Step-by-Step Solution

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