1. ## Word problem

Which of the following pairs of quantities vary directly?

a. the circumference of a cirlce and the diameter of the circle
b. the distance traveled in two hours and the average rate of travel
c.the number of gallons of gasoline bought and the cost of the purchase
d. the area of a circle and the radius of the circle

I think it is a,c and d. Is the answer correct?

Does vary directly mean that it will always be a linear equation?

Thanks to everyone for helping me and putting up with my random questions. I love doing word problems but I don't know much about algebra yet. so I am just trying to do the ones I can.

Thanks.

Vicky

2. Hello Vicky
Originally Posted by Vicky1997
Which of the following pairs of quantities vary directly?

a. the circumference of a cirlce and the diameter of the circle
b. the distance traveled in two hours and the average rate of travel
c.the number of gallons of gasoline bought and the cost of the purchase
d. the area of a circle and the radius of the circle

I think it is a,c and d. Is the answer correct?

Does vary directly mean that it will always be a linear equation?

Thanks to everyone for helping me and putting up with my random questions. I love doing word problems but I don't know much about algebra yet. so I am just trying to do the ones I can.

Thanks.

Vicky
A simple but effective way to test whether two quantities vary directly is this: if I double one quantity, do I double the other quantity? If the answer is yes, then they probably vary directly.

So (a) If you double the diameter, does the circumference double? Yes. So you're right.

(b) If you double the average rate of travel (in other words, the speed) does the distance you'll travel in two hours double also? Answer: yes. So you're not right - this does vary directly.

(c) If you buy twice as much gas, does it cost twice as much? Yes. So you're right here.

(d) If the radius of a circle is doubled, does the area double? No, it goes up by a factor of 4, because it's proportional to the square of the radius. So, you're not right on this one.

OK, now?