You're going on a 1211-mile trip, and your car gets about 29 miles per gallon. Gas prices along your route average $3.30. Estimate the cost of gasoline for this trip by rounding the distance to 1200 miles, the mileage to 30 miles per gallon, and the cost of gas to $3.00 per gallon. Calculate the answer without using estimation and compare the two results. (Round your answers to the nearest cent.)
+2446 The estimation underestimates by $18.60.
Let's think about what the question is asking. We have to compare an estimated value with the exact value. First, let's calculate the exact amount of gasoline it costs for this roadtrip. We can setup a proportion to solve for the amount of gallons we need for the entire trip:
\(\frac{1211mi}{xgal}=\frac{29mi}{1gal}\)
Cross multiply and solve for x, the amount of gallons for the entire roadtrip.
\(1211=29x\)
Divide by 29 on both sides:
\(x=\frac{1211}{29}\approx41.7586\)
29 does not divide into 1211 evenly. Here, we must round up the number of gallons we need. 41 gallons is not enough gallons to get us to our destination, but getting a fraction of a gallon is not practical, so we need 42 gallons. To calculate the amount of money it will cost for the roadtrip, multiply the amount of gallons by the amount it costs per gallon.
\(42gal*$3.30=$138.60\)
This is the exact cost of going to on this roadtrip. Now, let's calculate the estimated cost. We'll use the exact same process as above: setting up a proportion:
\(\frac{1200mi}{xgal}=\frac{30mi}{1gal}\)
Just like before, cross multiply and solve for x.
\(1200=30x\)
\(x=40gal\)
We don't need to round this number like we did before because this is the exact (no more and no less) gallons needed to get to this estimated destination. Now, multiply the amount of gallons by the amount it costs per gallon:
\(40gal*$3.00=$120.00\)
Now, we must compare. I'll compare the two answers by subtracting the two numbers to see how far the estimation was from the actual cost:
\($138.60-$120.00=$18.60\)
To compare, you can say that the estimation underestimated by $18.60.
