fambrini wrote:At the bakery, Lew spent a total of $6.00 per one kind of cupcake and one kind of doughnut. How many doughnuts did he buy?
1) The price of 2 doughnuts was $0.10 less than the price of 3 cupcakes.
2) The average (arithmetic mean) price of 1 doughnut and 1 cupcake was $0.35
Target question: How many doughnuts did Lew buy?
Let D = the NUMBER of donuts purchased.
Let C = the NUMBER of cupcakes purchased.
Let X = the PRICE per donut (in CENTS)
Let Y = the PRICE per cupcake (in CENTS)
ASIDE: Given that we have 4 different variables, we will likely need 4 equations to answer the target question.
Given: Lew spent a total of $6.00 for one kind of cupcake and one kind of doughnut.
In other words, Lew spent 600 CENTS
We can write:
DX + CY = 600
Okay that's 1 equation. When I SCAN the two statements, I can see that I will be able to create one equation for each statement.
This means we will have a total of 3 equations, which likely means the combined statements are insufficient.
Given this let's jump to ......
Statements 1 and 2 combined
From statement 1, we can write:
2X = 3Y - 10
From statement 2, we can write:
1X + 1Y = 70 (CENTS)
We can solve this system to get,
X = 40 and
Y = 30
When we can plug these values into our first equation,
DX + CY = 600, we get:
D(40) + C(30) = 600
Rewrite as:
40D + 30C = 600
Divide both sides by 10 to get:
4D + 3C = 60
There are several solutions to this equation. Here are two:
Case a: D = 3 and C = 16. In this case, the answer to the target question is
Lew bought 3 donuts
Case b: D = 6 and C = 12. In this case, the answer to the target question is
Lew bought 6 donuts
Since we cannot answer the
target question with certainty, the combined statements are NOT SUFFICIENT
Answer: E
Cheers,
Brent
