An event planner ordered a total of 30 gift baskets for a corporate conference. Standard g… — GMAT

An event planner ordered a total of $30$ gift baskets for a corporate conference. Standard gift baskets cost $\$25$ each, and Deluxe gift baskets cost $\$40$ each. If the total cost of all $30$ gift baskets was $\$900$ , how many Deluxe gift baskets were ordered?

$10$ Answer
B
$12$
C
$15$
D
$20$
E
$25$

Answer

The correct number of Deluxe gift baskets ordered is

10

By setting up the linear system

x + y = 30

and

25x + 40y = 900

, substituting

x = 30 - y

into the cost equation yields

750 + 15y = 900

, which solves directly to

y = 10

. Therefore,

10

Deluxe baskets were ordered.

Step-by-Step Solution

Define variables and set up the system of linear equations

Let

x

be the number of Standard baskets and

y

be the number of Deluxe baskets. Equation 1:

x + y = 30

. Equation 2:

25x + 40y = 900

The total number of baskets establishes a quantity relation, while the individual prices establish a cost relation.

Express

x

in terms of

y

using Equation 1

x = 30 - y

Isolating

x

allows direct substitution into the total cost equation to solve for

y

Substitute

x = 30 - y

into Equation 2 and solve for

y

25(30 - y) + 40y = 900 \implies 750 - 25y + 40y = 900 \implies 15y = 150 \implies y = 10

Simplifying the single-variable equation yields the exact number of Deluxe gift baskets.

Key Concept

Solving Systems of Linear Equations using Substitution or Elimination

Alternative Method

Use the elimination method: multiply the total quantity equation by

25

(

25x + 25y = 750

) and subtract it from the total cost equation (

25x + 40y = 900

) to get

15y = 150

, leading directly to

y = 10

Estimated Time:45s

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Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Alternative Method

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