An economical automobile can travel 416 miles on just 13 gallons of gasoline. How many
gallons of gasoline will be needed for a trip of 1792 miles?

56 gallons of gasoline

Step-by-step explanation:

So, we have 1792 miles to cover, and we need to know how much gallons we need to make that trip.

1 ) First, we need to figure out how much one gallon covers, find the unit rate.

          - 416 (miles) divided by 13 (gallons)= 32 (miles) One gallon fuels 32 miles of travel.

2) Next, we need to find how many gallons are needed for 1792 miles. That means we use the 32 we just found to replace the gallon in our division problem because it is in the same unit of measurement as the 1792.

          - 1792 (miles) divided by 32 (miles) = 56 (gallons) The answer is 56 gallons.

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4