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Video: Solving Word Problems Involving Ratios

Tim Burnham

Brian’s car can travel 570 miles on 15 gallons of gasoline. Using a ratio table, determine how many miles he can travel on 11 gallons.


Video Transcript

Brian’s car can travel five hundred and seventy miles on fifteen gallons of gasoline using a ratio table. Determine how many miles he can travel on eleven gallons. Now a ratio table is just simply a table including in this case gallons and miles or numbers, which are in the same proportion as the numbers we were given in the question. So in the question, we were told that if we have fifteen gallons, we can travel five hundred and seventy miles. Now we can put whatever numbers we want in here, but I’m gonna go for one five and ten. Now five is easy to calculate because it’s a third of fifteen. And then I can divide that by five to get one. If I double five, I get ten. And to get eleven gallons, I’m just gonna add together the values for one and ten. So let’s see fifteen divided by three gives us five.

So if I’m using only a third as much petrol, then I’m only gonna be able to travel a third as far. So I’ve got to calculate five hundred and seventy divided by three. Now you may be able to do that in your head. But if you can’t, you’ve got to do a little bit of a calculation. Here how many times does three go into five? Well it only goes once and one times three is three.

And the difference there five take away three is two, so we can out bring down the seven. So we’ve now got to work out how many times does three go into twenty-seven. Well three is going to twenty-seven nine times nine times three is twenty-seven. And twenty-seven take away twenty-seven is zero. Now I’m gonna bring down the next zero zero zero. So how many threes go into zero zero. So our answer is a hundred and ninety-three times a hundred. And ninety is five hundred and seventy.

So if we use a third as much gasoline we can only go a third as far. Third of fifteen is five a third of five hundred and seventy is a hundred and ninety. Well look I can now double five to get ten. So if I’ve got twice as much fuel, then I can go twice as far. Two times a hundred and ninety is three hundred and eighty.

So we’ve only got one more value to fill in in our table. Now how can I get one? Well I could divide five by five. I could divide ten by ten. Or I could divide fifteen by fifteen. Now the easiest of those three options really is dividing by ten. Starting up with ten gallons of fuel, if I only have a tenth as much fuel, I’ll only be able to go a tenth as far. So three hundred and eighty divided by ten is thirty-eight.

So now I’ve completed my ratio table. And I can ask my question “Determine how many miles we can travel on eleven gallons”. So to do eleven gallons, I’ve got one gallon plus ten gallons. So I could do thirty-eight miles plus three hundred and eighty. So thirty-eight plus three hundred and eighty. Eight plus zero is eight three and eight is eleven, so that’s one carry one. And three plus one is four, so eleven gallons would take me four hundred and eighteen miles. So there we have it. Our answer: four hundred and eighteen miles.