Hi All,

We're told that coffee is only sold in one pound bags, each pound of mild coffee costs $2.10 and each pound of hearty coffee costs $2.30. We're asked for the number of pounds of mild coffee that Garcia bought.

1) The total value of the coffee Garcia purchased was $17.80

Since each type of coffee costs a little more than $2, this $17.80 total means that there were likely 8-9 total pounds of coffee purchased. This severely limits the number of possible 'combinations' of coffee, so we can use a bit of 'brute force' math to get to the solution.

Multiples of $2.10: $2.10, $4.20, $6.30, $8.40, $10.50, $12.60, $14.70, $16.80

Multiples of $2.30: $2.30, $4.60, $6.90, $9.20, $11.50, $13.80, $16.10

So, how many different ways can you get to $17.80 using one value from each row (hint: you can 'count down' from $16.80 and try to find a multiple of $2.30 that will increase the sum to $17.80)?

$6.30 and $11.50

This is the only option that fits the given information - and the answer to the question is 3 pounds.

Fact 1 is SUFFICIENT

2) If Garcia had purchased 1 more pound of each type of coffee he would have spent $22.20

Purchasing one more pound of each type would have increased the total by $2.10+$2.30 = $4.40. The total in Fact 2 is $22.20, which is exactly $4.40 more than the $17.80 we were dealing with in Fact 1. Since Fact 1 had just one solution, spending $4.40 more can only lead to $22.20 from that one solution.

Fact 2 is SUFFICIENT

Final Answer:

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Rich

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