Arabica coffee costs $0.40 per ounce, while Robusta coffee costs $0.30

Question

Arabica coffee costs $0.40 per ounce, while Robusta coffee costs $0.30 per ounce. If a blend of Arabica and Robusta costs $0.33 per ounce, what percentage of the blend is Arabica?

A. 20%
B. 24%
C. 30%
D. 33%
E. 40%

M21-34

tarek99 · Accepted Answer

a= amount of arabica coffee
1-a = amount of robusta coffee. because if you subtract a from the 1 ounce, the remaining amount is robusta

therefore:
.4a + .3(1-a) = .33

.4a + .3 - .3a = .33
a= .3

therefore: .3/1 ounce = 30%. Therefore, the answer should be C

Bunuel · Answer

If the blend contains  A  ounces of Arabica and  R  ounces of Robusta then  \frac{A0.4 + R0.3}{A + R} = 0.33  or  0.07A = 0.03R  or  \frac{A}{R} = \frac{3}{7} . Hence  \frac{A}{(A + R)} = \frac{A}{(TOTAL)} = \frac{3}{(3 + 7)} = \frac{3}{10} = 30% .

Answer: C

pacifist85 · Answer

Hey, I followed sort of the same way as Bunuel, like this:

0,4A + 0,3R = 0,33(A+R)
0,4A + 0,3R = 0,33A + 0,33R
0,4A - 0,33A = 0,33R - 0,3R
0,07A = 0,03R
A/R = 0,03 / 0,07.

So, from here we see that the ratio of A to R is 3:7. So, if 10 is our whole blend, then A is 30%.  ANS C

mm229966 · Answer

0.4 - 0.33 / 0.33 - 0.3 = 7/3 => 3 part of 100 is 30%

kungfury42 · Answer

What a smart question, the 33% option is definitely a nice trap that even I admittedly fell for. It's very convenient to take 0.33 as 1/3rd without realizing that it is a terminating decimal and not the non-terminating and recurring decimal that $\overline{0.3}$ is. Here's how this must be done:

0.4A + 0.3B = 0.33(A+B)
0.4A + 0.3B = 0.33A + 0.33B
0.07A = 0.03B
A/B = 3/7
A/A+B = 3/10 = 30%

Therefore, A must be 30% of the mixture, option B.

0.4A + 0.3B = 0.33(A+B)
0.4A + 0.3B = 0.33A + 0.33B
0.07A = 0.03B
A/B = 3/7
A/A+B = 3/10 = 30%

Therefore, A must be 30% of the mixture, option B.

bumpbot · Answer

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Arabica coffee costs $0.40 per ounce, while Robusta coffee costs $0.30

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Arabica coffee costs $0.40 per ounce, while Robusta coffee costs $0.30

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