A science museum offers two ticketing options for groups. Option A is a flat group rate of… — SAT

A science museum offers two ticketing options for groups. Option A is a flat group rate of $125 plus$ 9.50 per person. Option B is a flat group rate of $50 plus$ 12.50 per person. For a group of $p$ people, Option A is less expensive than Option B. What is the minimum number of people in the group for this to be true?

Cevap: 26 people

Cevap

The minimum number of people in the group is 26.

To find when Option A is less expensive than Option B, we set up the inequality representing their respective costs:

125 + 9.5p < 50 + 12.5p

. Subtracting

9.5p

from both sides gives

125 < 50 + 3p

. Subtracting

50

from both sides yields

75 < 3p

. Dividing by

3

gives

p > 25

. Because the group must consist of a whole number of people, the minimum integer value of

p

that is strictly greater than

25

26

Adım Adım Çözüm

Write the inequality representing the cost comparison between the two ticketing options.

125 + 9.5p < 50 + 12.5p

Option A's cost must be strictly less than Option B's cost for Option A to be less expensive.

Isolate the variable

p

by subtracting

9.5p

and

50

from both sides of the inequality.

p > 25

Subtracting

9.5p

yields

125 < 50 + 3p

. Subtracting

50

yields

75 < 3p

. Dividing by

3

yields

p > 25

Identify the minimum integer value of

p

that satisfies the inequality.

Since the number of people must be a positive integer, the smallest integer strictly greater than

25

26

Anahtar Kavram

Solving linear inequalities in one variable and interpreting the solution set within a discrete real-world context.

Tahmini Süre:1m 30s

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