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In order to solve this problem you should know the equation for perimeter of a rectangle. If you don’t know it is 2W + 2L = P. Or in other words two lengths plus two widths equals the perimeter.
First, you should write your expressions for the length and width. Do NOT use L and W. You should only use one letter so you can solve the equation. Why don’t we choose to use W in our example. Now you must find the relationship between the length and width.
1. The length of a rectangle is 2 more then twice its width. The perimeter of the rectangle is equal to 40 Write an equation to solve for the perimeter in terms of the width. Then solve for L and W.
2W+2L=P (the 1st equation is the equation for the perimeter)
Now we take figure out that the lengths is 2w+2, so now we substitute 2w+2 for L which now gives us one variable to solve for. The equation is 2(W) +2(2W+2)=40. After you solve the equation you should get W=6 and L=14.
Example 2 - Basic equations
2. John and George earned a combined $500 working at a school fundraiser. John worked more hours than George and therefore generated $100 more than George.
First, we need to find a variable to represent George’s earnings, let’s choose G. You can only use ONE variable. Do not use J for John in the equation because you must write the equation with both George and John.From the word problem above we can now write our equations. We know that John and George earned a combined $500 so that translates to…J+G=500. Now that we have our two equations we can substitute G+100 for J. So our new equation is…G+ G+100=500.After you solve the equation you should get G=200, and J=300.
Example 3 - Consecutive integers
3. Ten times the first of three consecutive integers is equal to 2 more than 4 times the second.
There are a few different types of consecutive integers we must learn about first before we do the problem. There are (normal) consecutive integers and there are Even or Odd consecutive integers.Consecutive intergers are numbers such as 2,3,4. in order to write it in an equation you must write it as x,(x+1),(x+2). Consecutive even integers are, 2,4,6, and consecutive odd intergers are 3,5,7. To write BOTH consecutive even and odd you write x, (x+2), (x+4). Now that we know more about consecutive integers lets write out equation... 10x=4(x+1) +2. Now solve to get....x=1.
Example 4- Investment
Investment problems usually have simple annual interest instead of compound interest. The Interest formula is I=Prt. “I” stands for the interest on the original investment, P stands for the original investment (called Principle), r stands for the interest rate.
Note: since this equation is for ANNUAL interest (yearly) if you are not looking for the interest yearly you should change the equation so it is for example, 9 months is 9/12 of a year or 0.75. If you do not change the “r” rate and leave it as 1 you will get the WRONG ANSWER!
4.You put $2000 into an investment yielding 0.08 (remember to convert the percent to a decimal for the equation.) You left the money there for two years. How much interest did you collect after the end of that time?The equation is P= $2000, r= 0.08 and t=2 substituting these numbers for the letters I get….I= (2000) (0.08) (2).After you multiply the answer is… 320 so I=320, which means you earn $320 in interest!!
1. Joe makes twice as much as Larry in a week. Larry makes $300 a week. How much does Joe make in a week?
2. 8 times the second of 3 consecutive integers is equal to 4 less than 4 times the third.
3. The first number is 3 times the second number. The second number is 9, what is the first number?
4. 17 less than four times a number is 7 more than the same number.
Medium:
5. Carli and Marli worked a combined 20 hours at the fair. Carli worked four hours more than Marli. How many hours did Carli and Marli each work?
6. The length of a rectangle is 6 more than twice its width. The perimeter of the rectangle is equal to 228. Write an equation to solve for the perimeter in terms of the width. Then solve for L and W.
Hard:
7. REAL WORLD PROBLEM
You bought a 12-month certificate of deposit for $20,000. The certificate of deposit yields 5% per year. You leave your money at the bank for one year. How much interest did you collect after that one year?
8. REAL WORLD PROBLEM
You put $2,500 into an investment yielding 12%. You left the money in the bank for eight months. How much interest did you collect after the eight months?