5
algebra

A museum charges $15 for adults and $9 for children. One day, 180 people visited and paid $2,100 total. How many adults visited?

A

70 adults

B

75 adults

C

80 adults

D

85 adults

Correct Answer: D

Choice D is the correct answer. Let aa = adults and cc = children.

System: {a+c=18015a+9c=2100\begin{cases} a + c = 180 \\ 15a + 9c = 2100 \end{cases}

Step 1: From first: c=180−ac = 180 - a

Step 2: Substitute: 15a+9(180−a)=210015a + 9(180 - a) = 210015a+1620−9a=210015a + 1620 - 9a = 21006a=4806a = 480a=80a = 80

15(80)+9(100)=1200+900=210015(80) + 9(100) = 1200 + 900 = 2100 ✓

💡 Strategic Tip: Revenue = tickets × price.

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Linear Functions Set 59