1
algebra

A candy store sells chocolate bars for $2 each and lollipops for $0.50 each. Marcus bought 20 items total for $25. How many chocolate bars did he buy?

A

10 chocolate bars

B

12 chocolate bars

C

15 chocolate bars

D

8 chocolate bars

Correct Answer: A

Choice A is the correct answer. Let cc = chocolate bars and ll = lollipops.

System: {c+l=202c+0.5l=25\begin{cases} c + l = 20 \\ 2c + 0.5l = 25 \end{cases}

Step 1: From first equation: l=20cl = 20 - c

Step 2: Substitute: 2c+0.5(20c)=252c + 0.5(20 - c) = 252c+100.5c=252c + 10 - 0.5c = 251.5c=151.5c = 15c=10c = 10

Solution: 10 chocolate bars (and 10 lollipops)

Verification: 10+10=2010 + 10 = 20 ✓ and 2(10)+0.5(10)=20+5=252(10) + 0.5(10) = 20 + 5 = 25

💡 Strategic Tip: Convert decimals to fractions if it helps: 0.5=120.5 = \frac{1}{2}.

Choice B is incorrect because 2(12)+0.5(8)=24+4=28 eq252(12) + 0.5(8) = 24 + 4 = 28 \ eq 25.

Choice C is incorrect because 2(15)+0.5(5)=30+2.5=32.5 eq252(15) + 0.5(5) = 30 + 2.5 = 32.5 \ eq 25.

Choice D is incorrect because 2(8)+0.5(12)=16+6=22 eq252(8) + 0.5(12) = 16 + 6 = 22 \ eq 25.