Rates,+Work,+and+Percent+Problems


 * Rates, Work & Percent Problems ||
 * || **1.** || Sara is mixing together a fruit punch for a party. She's made 6 gallons of punch with a mixture of 50% juice. Her mother tells her to change it to a mixture of 70% juice.

How much fruit juice should be added to make the mixture 70% fruit juice (round to the nearest hundredth)? || ||

Write your response here: (show your work)
 * **A.** || ||
 * **B.** || ||
 * **C.** ||  ||
 * **D.** || ||

SHOW IN BOX Let x stand for the unknown amount of juice that needs to be added. Currently, there are 3 gallons of juice in the 6 gallons of fruit punch. Set up the problem in equation form.
 * Explanation:**
 * (3 + x)/(6 + x) || = || 70% ||
 * (3 + x)/(6 + x) || = || 0.7 ||
 * 4.2 + 0.7x || = || 3 + x ||
 * 0.3x || = || 1.2 ||
 * x || = || **4 gallons** ||


 * || **2.** || Mrs. Carter owns a shop specializing in obscure blends of tea. She has combined 1 pound of Darjeeling with 4 pounds of Earl Grey, for a 5-pound mixture that is 20% Darjeeling. After tasting it, she decided to change the mixture to 60% Darjeeling. How much Darjeeling does she need to add to bring it up to the 60%? || ||

Write your response here: (show your work)
 * **A.** || ||
 * **B.** || ||
 * **C.** || ||
 * **D.** ||  ||

First, set up the problem in equation form. Now, solve for x.
 * Explanation:**SHOW IN BOX
 * (1 + x)/(5 + x) || = || 0.6 ||
 * (1 + x)/(5 + x) || = || 0.6 ||
 * (10 + 10x)/(5 + x) || = || 6 ||
 * 30 + 6x || = || 10+10x ||
 * 4x || = || 20 ||
 * x || = || **5 lb** ||


 * || **3.** || Hal is mixing bug spray for his roses. He has one gallon with a mixture of 90% water and 10% chemical. However, he needs a mixture that is 95.5% water. How much water should be added to the mixture to make it 95.5% water? || ||

Write your response here: (show your work)
 * **A.** || ||
 * **B.** || ||
 * **C.** ||  ||
 * **D.** || ||

Set up the problem as an equation, then solve for x.
 * Explanation:**SHOW IN BOX
 * (0.90 + x)/(1+x) || = || 0.955 ||
 * 0.90 + x || = || 0.955 + 0.955x ||
 * 0.955 - 0.90 || = || 1x - 0.955x ||
 * 0.055 || = || 0.045x ||
 * x || = || **1.22 gallons** ||


 * || **4.** || Josh is mixing together concrete to build a brick wall. He's made 6 gallons of concrete with a mixture of 50% water. The instructions on the bag of concrete say the mixture should be made of 70% water.

How much water should be added to make the mixture 70% water (round to the nearest hundredth)? || ||

Write your response here: (show your work)
 * **A.** || ||
 * **B.** || ||
 * **C.** || ||
 * **D.** ||  ||

Let //x// stand for the unknown amount of water that needs to be added. Currently, there are 3 gallons of water in the 6 gallons of concrete. Set up the problem in equation form.
 * Explanation:**SHOW IN BOX



Therefore, **4 gallons** should be added to the mixture.


 * || **5.** || Sandra is mixing bleach and water so she can clean her house. She has a gallon bottle with a mixture of 60% bleach and 40% water. However, she needs the mixture to be 44% water. How much water should be added to the mixture to make it 44% water? (Round to the nearest hundredth) || ||

Write your response here: (show your work)
 * **A.** || ||
 * **B.** || ||
 * **C.** || ||
 * **D.** ||  ||

Set up the problem as an equation, then solve for x.
 * Explanation:**SHOW IN BOX
 * (0.40 + x)/(1+x) || = || 0.44 ||
 * 0.40 + x || = || 0.44 + 0.44x ||
 * 0.44 - 0.40 || = || 1x - 0.44x ||
 * 0.04 || = || 0.56x ||
 * x || = || **0.07 gallons** ||


 * || **6.** || Kathleen is making a cup of coffee. She has added 4 ounces of cream to 16 ounces of coffee, for a 20-ounce mixture that is 20% cream. After tasting it, she decided to change the mixture to 25% cream. How much cream does she need to add to bring it up to 25% cream? || ||

Write your response here: (show your work)
 * **A.** || ||
 * **B.** || ||
 * **C.** ||  ||
 * **D.** || ||

First, set up the problem in equation form. Now, solve for x.
 * Explanation:**SHOW IN BOX
 * (4 + x)/(20 + x) || = || 0.25 ||
 * (4 + x)/(20 + x) || = || 0.25 ||
 * (400 + 100x)/(20 + x) || = || 25 ||
 * 500 + 25x || = || 400 + 100x ||
 * 75x || = || 100 ||
 * x || = || **1 1/3 oz** ||


 * || **7.** || Cathy is babysitting her little brother, who escapes out the door when she isn't looking. She discovers that he's gone 15 minutes later and runs after him. If the little brother can run 4 mph and Cathy can run 8 mph, how long will it take Cathy to catch up with her little brother? || ||

Write your response here: (show your work)
 * **A.** || ||
 * **B.** || ||
 * **C.** || ||
 * **D.** ||  ||

The little brother has a 15 minute, or 1/4 hr, head start. When Cathy goes after him, he will already be 4 × (1/4) = 1 mile away. Let t be the time in hours. The brother will be at 1 + 4t, and Cathy will be at 8t when she goes after him. To find out how long it takes to catch her brother:
 * Explanation:**SHOW IN BOX
 * 1 + 4t || = || 8t ||
 * 1 || = || 4t ||
 * t || = || **1/4 hr** ||


 * || **8.** || Tom and Jerry have to sort and organize all the nails on their father's workbench. Tom can sort 210 nails in 2 hours. Jerry can sort 90 nails in 3 hours. How long will it take them to sort 700 nails if they work together (round to the nearest hundredth)? || ||

Write your response here: (show your work)
 * **A.** || ||
 * **B.** ||  ||
 * **C.** || ||
 * **D.** || ||

First, set up the problem in equation form. Now solve for t.
 * Explanation:**SHOW IN BOX
 * (210/2)t + (90/3)t || = 700 ||
 * 105t + 30t || = || 700 ||
 * 135t || = || 700 ||
 * t || = || **5.19 hrs** ||


 * || **9.** || Two runners left the school and ran in opposite directions on the main street. If one runner averaged 4 mph and the other averaged 7 mph, how long was it before they were 30.8 miles apart? || ||

Write your response here: (show your work)
 * **A.** ||  ||
 * **B.** || ||
 * **C.** || ||
 * **D.** || ||

Let t = the time the two runners run until they are 30.8 miles apart. The runners will be 30.8 miles apart in **2.8 hours**.
 * Explanation:**SHOW IN BOX
 * First runner's rate || = || 4t ||
 * Second runner's rate || = || 7t ||
 * Miles apart || = || 30.8 ||
 * 4t + 7t || = || 30.8 ||
 * 11t || = || 30.8 ||
 * t || = || 2.8 ||
 * 4t + 7t || = || 30.8 ||
 * 11t || = || 30.8 ||
 * t || = || 2.8 ||


 * || **10.** || Beth and Carla are working together to make 500 party favors for the holidays. Beth can make 150 favors in two hours. Carla can make 75 favors in one hour. How long will it take them to make all 500 favors (round to the nearest hundredth)? || ||

Write your response here: (show your work)
 * **A.** || ||
 * **B.** || ||
 * **C.** || ||
 * **D.** ||  ||

First, set up the problem in equation form. Now solve for t.
 * Explanation:**SHOW IN BOX
 * (150/2)t + (75/1)t || = || 500 ||
 * 75t + 75t || = || 500 ||
 * 150t || = || 500 ||
 * t || = || **3.33 hrs** ||