3
algebra

A baker needs to mix flour that costs $2 per pound with flour that costs $5 per pound to create 60 pounds of a mixture that costs $3.50 per pound. How many pounds of the $2 flour are needed?

A

25 pounds

B

30 pounds

C

35 pounds

D

40 pounds

Correct Answer: B

Choice B is the correct answer. Let xx = pounds of $2 flour and yy = pounds of $5 flour.

System: {x+y=602x+5y=3.50(60)\begin{cases} x + y = 60 \\ 2x + 5y = 3.50(60) \end{cases}

Step 1: Simplify: {x+y=602x+5y=210\begin{cases} x + y = 60 \\ 2x + 5y = 210 \end{cases}

Step 2: From first: y=60xy = 60 - x

Step 3: Substitute: 2x+5(60x)=2102x + 5(60 - x) = 2102x+3005x=2102x + 300 - 5x = 2103x=90-3x = -90x=30x = 30

Solution: 30 pounds of $2 flour (and 30 pounds of $5 flour)

Verification: 2(30)+5(30)=60+150=2102(30) + 5(30) = 60 + 150 = 210 ✓ and 21060=3.50\frac{210}{60} = 3.50

💡 Strategic Tip: The mixture's total value = sum of individual values.

Choice A is incorrect because 2(25)+5(35)=50+175=225 eq2102(25) + 5(35) = 50 + 175 = 225 \ eq 210.

Choice C is incorrect because 2(35)+5(25)=70+125=195 eq2102(35) + 5(25) = 70 + 125 = 195 \ eq 210.

Choice D is incorrect because 2(40)+5(20)=80+100=180 eq2102(40) + 5(20) = 80 + 100 = 180 \ eq 210.