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How Do You Use an Equation with Consecutive Numbers to Solve a Word Problem?

Mrs. Jenkins has five children. Her youngest child is two years old. The next three children have consecutive ages. Her oldest child is two years older than the second oldest. If the combined age of her children is 41, what are the ages of Mrs. Jenkins' children?

Summary

  1. 2 is the age of the youngest
  2. If we let 'a' be the age of the 2nd youngest child, we can find the remaining children's ages
  3. 8, 9, 10, and 12 are the ages of the other children

Notes

    1. So there are 3 children that have ages one year apart
    1. 'a' is a variable representing the 2nd youngest child's age
    1. Remember that the 2nd youngest child is the youngest of the 3 consecutively aged children
    2. 'a' is a variable representing the 2nd youngest child's age
    1. The 2nd oldest child is the oldest of the 3 consecutively aged children
    1. We will just add on 2 years to whatever we get for the age of the 2nd oldest child
    2. The 2nd oldest child is the oldest of the 3 consecutively aged children
    1. In other words, we can figure out each child's age using the youngest child's age and the variable 'a'
    1. This was given to us
    1. We defined 'a' ourselves, making it a variable to represent the 2nd youngest child's age
    1. Since the 3rd youngest is one consecutive year older than the 2nd youngest, that child's age is 'a+1'
    2. 'a' is a variable representing the 2nd youngest child's age
    1. Since the 4th youngest is one consecutive year older than the 3rd youngest, that child's age is 'a+2'
    2. We just defined the age of the 3rd youngest as 'a+1'
    3. 'a' is a variable representing the 2nd youngest child's age
    1. We just defined the age of the 4th youngest as 'a+2'
    2. 'a' is a variable representing the 2nd youngest child's age
    1. Adding 2 years to the 4th oldest child's age will give us the age of the oldest child
    2. We just defined the age of the 4th youngest as 'a+2'
    3. 'a' is a variable representing the 2nd youngest child's age
    1. 'Combine' just means we want to add all the expressions together and set them equal to something
    1. So we'll set the combined ages equal to 41
    2. 'Combine' just means we want to add all the expressions together and set them equal to something
    1. 'Combine' just means we want to add all the expressions together and set them equal to something
    1. We do this since the problem says their ages combined equals 41
    2. 'Equations' refers to all the expressions that we set each child's age to
    1. Grouping the like terms together will make it easier to solve the equation
    1. 2+1+2+4 = 9
    2. a+a+a+a = 4a
    1. 'a' is a variable representing the 2nd youngest child's age
    1. Subtracting '9' will give us the 'a' term on one side by itself
    2. 'a' is a variable representing the 2nd youngest child's age
    1. Dividing by '4' will cancel out the multiplication by '4' on the left side, giving us 'a' alone
    2. 32/4 = 8
    1. 'a' is a variable representing the 2nd youngest child's age
    1. This was given to us
    1. '8' was the answer we got for 'a'
    1. 8+1 = 9
    2. '8' was the answer we got for 'a'
    1. 8+2 = 10
    2. '8' was the answer we got for 'a'
    1. 8+4 = 12
    2. '8' was the answer we got for 'a'
    1. '8' was the answer we got for 'a'
    1. Our first combined equation was '2+a+(a+1)+(a+2)+(a+4) = 41'
    2. '8' was the answer we got for 'a'
    1. 8+4=12
    2. 8+2=10
    3. 8+1=9
    1. 2+8+9+10+12 = 41