Question

Some word problems in this chapter involve one "easy equation", usually found by translating a simple relationship between x and y (like one is twice the other or that they add to a given number). The second linear equation often uses a "rate times quantity" formula. This is true for • distance problems (rate time = distance) • mixture problems (percent concentration amount of solution = amount of concentrate) • money problems (value of one item = how many items = total value) Using a chart or drawings can help organize the different quantities. The actual equation you get depends on extra information; look for words like "total" to add, or "equal" to set them equal. Be careful with mixture problems since you will often need to multiply "rate times quantity" for the final mixture, not just add to a total. Here is an example, then you need to solve a similar problem, showing 1. Make a chart or drawing, and state what your variables represent. Be clear and include any units. 2. Write the "easy equation". 3. Write the equation that involves multiplying rates and quantities, then usually add if appropriate (if know total). 4. Solve algebraically. I want you to use the Addition Method, since the Week 7 had you use substitution. 5. State the full solution in sentence form, including any units. EXAMPLE: A 20% acid solution is mixed with a 60% acid solution to make 600 liters of a 50% acid solution. How much of each solution was used? 1. X = amount of 20% solution, in liters 600 Y= amount of 60% solution, in liters 60% 50% 20% 60% solution solution 50% solution Amount of solution in liters Amount of acid in 0.20x 0.60y liters 20% y 600 ? For this problem, I like to call the "easy" equation the "no spill" equation. As you pour the two solutions together into the final container, if you don't spill the quantities should add up.

Answer 1

X = The amount that was invested in 1st account which has 8% interest rate Y = The amount that was invested in and account which has 5% interest rare. list account 8% interest rare and accountt total 5% interest amount: rare 10800 Y 795 Amount given X Interest 2 ? 2. x + y = 10 800 3. formula is We know, the simple interest Interest Principal amount x Interest rate x time So, Interest from 1st account = 0.08 x 10o Interest from the 2nd account Y x 5 100 = 0.05 y 0.08 X + 0.05 Y = 795

4. To solve the system, We clear out the decimals from the and equation by multiplying by 100. Also we multiply the equation by negative 8 and adding them a Ist we get - 8x 8Y 86400 8 X +5Y 79500 6900 - 3y = 6900 Y = (2.300 3 then from O, x + y = 10800 x= 10800 – 2300 = 8500 5 SOLUTION! $ 8500 Was invested in the 1st account. account. invested in the and 2300 ways