So I have 4 questions. We were doing ratios in class and we have to figure out either the part or the total;
1. Katie and May took turns driving to Chicago. May drove 5 out of 11 miles. By the time they reached Chicago, May had driven 12 less miles than Katie. How many miles did Katie drive?
2. Teresa built a gaming website. The website had a total of 75 visitors on Monday. 7 out of every 15 visitors played flying games. The other visitors played driving games. How many visitors played driving games?
3.Joshephina spends 3 out of every 10 dollars she earns on books. She uses the rest of the money to buy clothes. Last month, she spent $27 on books. How much money did she spend on clothes?
4. For every 8 games the Hometown Heroes played the team won 5 of them. If they won 12 more games than they lost, how many games did they win?
if you could answer asap, that would be great!
Thanks in advance <3
just set up equations to fit the facts. For example,
#1
m/k = 5/6
m = k-12
so, (k-12)/k = 5/6
#2
7/15 = f/75
d = 75-f
what do you get for the others?
Sure! I'll be happy to help you with these questions. Let's solve them one by one:
1. Katie and May took turns driving to Chicago. May drove 5 out of 11 miles. By the time they reached Chicago, May had driven 12 fewer miles than Katie. How many miles did Katie drive?
To solve this, we can set up a ratio. May drove 5 out of 11 miles, so the ratio of May's miles to the total miles is 5:11. Since May drove 12 fewer miles than Katie, we can represent Katie's miles as x + 12, where x is the number of miles Katie drove.
Setting up the equation, we have:
5/11 = (x + 12)/x
To solve for x, we can cross-multiply:
5x = 11(x + 12)
5x = 11x + 132
-6x = 132
x = -22
Since distance cannot be negative, we discard the negative solution. Therefore, Katie drove x = -22 miles, which means Katie drove 22 miles.
2. Teresa built a gaming website. The website had a total of 75 visitors on Monday. 7 out of every 15 visitors played flying games. The other visitors played driving games. How many visitors played driving games?
To find the number of visitors who played driving games, we need to subtract the visitors who played flying games from the total number of visitors.
The ratio of visitors who played flying games to the total visitors is 7:15. We can set up the ratio:
7/15 = visitors who played flying games / total visitors
Cross-multiplying, we get:
7 * total visitors = 15 * visitors who played flying games
7 * total visitors = 15 * (visitors - visitors who played driving games)
Now, we substitute the total number of visitors with 75:
7 * 75 = 15 * (visitors - visitors who played driving games)
525 = 15 * (visitors - visitors who played driving games)
Next, we distribute and isolate "visitors - visitors who played driving games":
525 = 15 * visitors - 15 * visitors who played driving games
525 - 15 * visitors = -15 * visitors who played driving games
15 * visitors - 525 = 15 * visitors who played driving games
Now, we can solve for the visitors who played driving games:
visitors who played driving games = 15 * visitors - 525
visitors who played driving games = 15 * 75 - 525
visitors who played driving games = 1125 - 525
visitors who played driving games = 600
Therefore, 600 visitors played driving games.
3. Joshephina spends 3 out of every 10 dollars she earns on books. She uses the rest of the money to buy clothes. Last month, she spent $27 on books. How much money did she spend on clothes?
To find the money spent on clothes, we need to subtract the money spent on books from the total earnings.
The ratio of money spent on books to the total earnings is 3:10. We can set up the ratio:
3/10 = $27 / total earnings
Cross-multiplying, we get:
3 * total earnings = 10 * $27
3 * total earnings = $270
Now, we solve for total earnings:
total earnings = $270 / 3
total earnings = $90
Since Joshephina spent $27 on books, we subtract that amount from the total earnings to find the money spent on clothes:
money spent on clothes = total earnings - money spent on books
money spent on clothes = $90 - $27
money spent on clothes = $63
Therefore, Joshephina spent $63 on clothes.
4. For every 8 games the Hometown Heroes played, the team won 5 of them. If they won 12 more games than they lost, how many games did they win?
Let's assume the number of games the Hometown Heroes played is x. According to the ratio, they won 5 out of every 8 games played.
The ratio of games won to total games played is 5:8. We can set up the equation:
5/8 = games won / total games played
Cross-multiplying, we get:
5 * total games played = 8 * games won
5 * total games played = 8 * (games won - games lost + 12)
5 * total games played = 8 * (games won - (games won - 12) + 12)
5 * total games played = 8 * (games won - games won + 12 + 12)
5 * total games played = 8 * 24
Now, we solve for the total games played:
total games played = (8 * 24) / 5
total games played = 192 / 5
total games played = 38.4
Since the number of games played cannot be a decimal, we round down to the nearest whole number. Therefore, the Hometown Heroes played 38 games.
Now, to find the number of games won, we can substitute the value of total games played into the equation:
games won = (5 * total games played) / 8
games won = (5 * 38) / 8
games won = 190 / 8
games won = 23.75
Since the number of games won cannot be a decimal, we round down to the nearest whole number. Therefore, the Hometown Heroes won 23 games.
I hope this helps!