Question

Carrots sell for $2.10 per pound, and crackers sell for $2.90 per pound. Glen bought some carrots and some crackers. The total weight was 2.3 pounds and cost $6.03.

How many pounds of carrots and how many pounds of crackers did Glen buy

Answer 1

Is glen able to buy 1/2 pounds of anything?

Answer 2

Lets call the carrots 'c' and the crackers 'k'. From the question we know that:
\[c+k=2.3\] and \[2.1c+2.9k=6.03\]

We can solve this by getting everything in terms of either 'c' or 'k'.:
\[c+k=2.3\]\[c=2.3-k\]
Now we can substitute this into the second equation:
\[2.1c+2.9k=6.03\]\[2.1(2.3-k)+2.9k-6.03\]\[4.83-2.1k+2.9k=6.03\] and solve for k \[0.8k=1.2\]\[k=1.5\]

We now know that he bought 1.5lbs of crackers. We also know that he bought a total weight of 2.3lbs. So using our first equation:\[c+k=2.3\]\[c+1.5=2.3\]\[c=0.8lbs\]
Glen bought 0.8lbs of carrots and 1.5 pounds of crackers.

We can check this using our money equation. \[2.1c+2.9k=6.03\]\[2.1(0.8)+(2.9)(1.5)=6.03\]\[1.68+4.35=6.03\]\[6.03=6.03\] Check is good.