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How Do You Solve a Word Problem Using a Multi-Step Equation?

Jack and Jill were catching tadpoles. At first, Jill caught nine times three more than Jack caught. Jack was upset, released half of Jill's tadpoles, and then six times as many as Jack caught swam away. If, after all this, Jill only had 3 tadpoles left, how many tadpoles did Jack catch?

Summary

  1. 't' is a variable representing the number of tadpoles that Jack ended up with

Notes

    1. 't' is a variable representing the number of tadpoles that Jack ended up with
    1. 't' is a variable representing the number of tadpoles that Jack ended up with
    1. Remember that 't' represents what Jack caught
    1. 't' is a variable representing the number of tadpoles that Jack ended up with
    1. 't' is a variable representing the number of tadpoles that Jack ended up with
    1. 't' is a variable representing the number of tadpoles that Jack ended up with
    1. 't' is a variable representing the number of tadpoles that Jack ended up with
    1. 't' is a variable representing the number of tadpoles that Jack ended up with
    1. '((9(t+3))/2) - 6t' is our expression
    2. 't' is a variable representing the number of tadpoles that Jack ended up with
    1. Remember that our expression '((9(t+3))/2) - 6t' represents the number of tadpoles Jill ended up with
    2. 't' is a variable representing the number of tadpoles that Jack ended up with
    1. Since '((9(t+3))/2) - 6t' and '3' both equal the number of tadpoles Jill ended up with, we can set them equal
    2. 't' is a variable representing the number of tadpoles that Jack ended up with
    1. '((9(t+3))/2) - 6t = 3' is our equation
    2. 't' is a variable representing the number of tadpoles that Jack ended up with
    1. 't' is a variable representing the number of tadpoles that Jack ended up with
    1. This will allow us to solve for 't'
    2. Remember that 't' represents the number of tadpoles Jack caught
    1. This is the first step to getting 't' by itself on one side
    2. Remember that 't' represents the number of tadpoles Jack caught
    1. This is the first step to getting 't' by itself on one side
    2. Adding '6t' to both sides cancels out the '-6t' on the left and adds a '6t' to the right side
    3. Remember that 't' represents the number of tadpoles Jack caught
    4. (9(t+3)/2) = 3+6t
    1. Multiplying by '2' cancels out the division by '2' on the left side and creates the product '(3+6t)2' on the right
    2. Remember that 'product' means multiplication
    1. 9(t+3) = (3+6t)2
    2. Multiplying by '2' cancelled out the division by '2' on the left side and created the product '(3+6t)2' on the right
    1. 9(t+3) = (3+6t)2
    2. 'Distribute' means to multiply what's outside of the parentheses by each term inside the parentheses
    1. 9t+27 = 6+12t
    2. Notice we have 't' on both sides now
    3. Remember that 't' represents the number of tadpoles Jack caught
    1. 9t+27 = 6+12t
    2. We have 't' on both sides at this point
    3. Remember that 't' represents the number of tadpoles Jack caught
    1. This will cancel out the '9t' on the left and take '9t' away from the '12t' on the right
    1. 27 = 6+3t
    1. 21 = 3t
    1. Remember that 't' represents the number of tadpoles Jack caught
    1. 7 = t
    2. Remember that 't' represents the number of tadpoles Jack caught
    1. Since 't = 7', Jack caught 7 tadpoles
    1. '((9(t+3))/2) - 6t = 3' is our original equation
    2. Any time 't' occurs in the equation, use the value '7' instead
    1. (9(7+3))/2 - 6•7
    1. Does '(9(7+3))/2 - 6•7' equal 3?
    1. 7+3 = 10
    2. 9(10) = 90
    1. (90/2) - 6•7 = (90/2) - 42
    1. (90/2) = 45
    2. 45-42 = 3
    3. We have '3' on both sides so we know we did everything correctly