10.5 Honors Assignment

Rate Problem: Jeff and Lucy have been asked to wash their mom’s minivan. It takes Jeff 2 hours to wash the van by himself, and it takes Lucy 1.5 hours to wash the van by herself. How long will it take Jeff and Lucy to wash the van if they work together? a. What equation is used to solve this problem? What does each variable represent? equation is (J+L)/2= hrs. j=jeff l=lucy b. Identify the given information. Lucy washes 1/1.5 = 2/3 van/hour Jeff washes 1/2 van per hour c. Enter the given information into the equation.
(2hr+1.5hrs)/2=hrs
d. Solve the equation.
3.5hrs/2=1.75hrs
1¾ hours e. State the solution.
The solution is 1¾ hours

Interest Problem: Julian deposits money into two different savings accounts. He deposits $600 more into Account B than Account A. After a certain amount of time, Account A has earned $180 at a rate of 4%, and Account B has earned $375 at a rate of 5%. How much did Julian initially deposit into each account? a. What equation is used to solve this problem? What does each variable represent? b. Identify the given information. What do you know about P? c. Enter the given information into the equation. d. Solve the equation. e. State the solution.
Let the deposit in Account A be x
4% of x = 180
Assuming the deposit is for one year, x = 4,500
Deposit in Account B
= x + 600
= 5100
Interest at 5% for one year
= 255
Interest earned as per the problem is 375
= 255 x 1.47
The deposit in Account B is $7,500
The deposit in Account A is $6,615
Mixture Problem: Addison is mixing hummingbird food to fill her feeders. Ideally, the hummingbird food should contain 25% sugar. Addison remembers that she has 8 ounces of leftover hummingbird food that contains 35% sugar. She decides to mix some diluted food to add to the leftover food. If the diluted food contains 10% sugar, how much should she add to the food with 35% sugar to get the ideal hummingbird food with