Bunuel wrote:
Last year, if Arturo spent a total of $12,000 on his mortgage payments, real estate taxes, and home insurance, how much did he spend on his real estate taxes?
Let M, R, and H be the amounts that Arturo spent on mortgage payments, real estate taxes, and home insurance, respectively.
Given: M + R + H = 12,000.
Question: R??
(1) Last year, the total amount that Arturo spent on his real estate taxes and home insurance was 33 1/3 percent of the amount that he spent on his mortgage payments --> 33 1/3 percent is 1/3 rd, thus given that R + H = M/3 --> M + R + H = M + M/3 = 12,000 --> M = 9,000 --> R + H = 12,000 - 9,000 = 3,000. R can take more than one value. Not sufficient.
(2) Last year, the amount that Arturo spent on his real estate taxes was 20 percent of the total amount he spent on his mortgage payments and home insurance --> given that R = (M + H)/5 --> 5R = M + H --> M + R + H = 5R + R = 12,000 --> 6R = 12,000 --> R = 2,000. Sufficient.
Answer: B.
when it says "Last year, the total amount that Arturo spent on his
real estate taxes and home insurance was 33 1/3 percent of the amount that he spent on his mortgage payments "
I expressd the red part like this (R+H)
0.30 = M why this equality didn't work ?
Same question applies for second statement "Last year, the amount that Arturo spent on his real estate taxes was
20 percent of the total amount he spent on his mortgage payments and home insurance "
i expressed the red part of sentance like this (M+H)0.20= R
here again it didnt work my equality
why ?
what is the difference the way bunuel expressed
R + H = M/3, R = (M + H)/5 and my equalities
(R+H)0.30 = M , (M+H)0.20= R 1st statement: R+H = \(\frac{33+\frac{1}{3}}{100}* M = \frac{1}{3} * M\) --> (R+H)*
2nd statement: \(R=\frac{20}{100}*(M+H)=\frac{1}{5}*(M+H)=0.2*(M+H)\) --> Legend
's expression and your expression are the same. You're right in this case.