Thread: help with setting up equations

Q1) The grocery store parking lot that will hold 1000 vehicles. 2/5 of the parking spaces are for cars. When you went to buy groceries, there were 200cars and some trucks in the parking lot. The parking lot was 3/4 full. How many trucks were in it?

A: Since 2/5 of the 1000 parking spaces are for cars, we know there are 400 spaces for cars and 600 for trucks. If 200 hundred cars are in the parking lot, then there are 800 open spots that can be filled with trucks. But, we are told 3/4 of the parking lot is filled, so 750 spots are filled. Since, 200 are filled by cars, 550 are filled by trucks. Correct?

Q2) Justin is making snowballs to build a fort on the winter break. Justin can build 15 snowballs in an hour but 2 snowballs melt every 15 minutes. How long will it take him to build 210 snowballs?

A: We are given that, every 60 minutes Justin makes 15 snowballs, but out of the 15 snowballs made in that 60 minutes 8 of them melt. Therefore, Justin is making snowballs at a rate of 7 snowballs every 60 minutes. This gives the proportion:

7/60=210/x, since we want to know the time it takes. So x=1800 minutes.

Do these answers look ok?

Originally Posted by EPZ

Q1) The grocery store parking lot that will hold 1000 vehicles. 2/5 of the parking spaces are for cars. When you went to buy groceries, there were 200cars and some trucks in the parking lot. The parking lot was 3/4 full. How many trucks were in it?

A: Since 2/5 of the 1000 parking spaces are for cars, we know there are 400 spaces for cars and 600 for trucks. If 200 hundred cars are in the parking lot, then there are 800 open spots that can be filled with trucks. But, we are told 3/4 of the parking lot is filled, so 750 spots are filled. Since, 200 are filled by cars, 550 are filled by trucks. Correct?

Correct, assuming there are only cars and trucks.

Q2) Justin is making snowballs to build a fort on the winter break. Justin can build 15 snowballs in an hour but 2 snowballs melt every 15 minutes. How long will it take him to build 210 snowballs?

A: We are given that, every 60 minutes Justin makes 15 snowballs, but out of the 15 snowballs made in that 60 minutes 8 of them melt. Therefore, Justin is making snowballs at a rate of 7 snowballs every 60 minutes. This gives the proportion:

7/60=210/x, since we want to know the time it takes. So x=1800 minutes.

Do these answers look ok?

This is a pretty dodgy question. If 8 of the snowballs he made in that hour melt, why doesn't the other snowballs made in previous hours melt?

Ignoring that you are also correct.

Originally Posted by Gusbob

This is a pretty dodgy question. If 8 of the snowballs he made in that hour melt, why doesn't the other snowballs made in previous hours melt?

Ignoring that you are also correct.

Yeah, that's what was bothering me.

I have another question:

Q) The recipe for mint chocolate ice cream requires two 1/4 cups of cream for 5 people. You need ice cream for 8 people. How much cream will you need?

A: We need 1/2 a cup of cream for 5 people. So, the proportion is:

cups/number of people; thus, (1/2)/5=(1/x)/8 iff 1/10=1/(x)8. So, x=4/5 cup of cream.

???

Thanks very much for your time.

Originally Posted by EPZ

I have another question:

Q) The recipe for mint chocolate ice cream requires two 1/4 cups of cream for 5 people. You need ice cream for 8 people. How much cream will you need?

A: We need 1/2 a cup of cream for 5 people. So, the proportion is:

cups/number of people; thus, (1/2)/5=(1/x)/8 iff 1/10=1/(x)8. So, x=4/5 cup of cream.

Correct again. I really need to read carefully next time.