3 Solving Application Problems

R.1 Fractions 3.3 Solving Application Problems with One Unknown Quantity Objectives Translate word phrases into algebraic expressions. Translate sentences into equations. Solve application problems with one unknown quantity.

Translate word phrases into algebraic expressions. Write each phrase as an algebraic expression. Use x as the variable. Example Words Algebraic Expression A number plus 2 The sum of 8 and a number 5 more than a number A number increased by 6 9 less than a number A number subtracted from 3 A number decreased by 4 10 minus a number

Translate word phrases into algebraic expressions. Write each phrase as an algebraic expression. Use x as the variable. Example Words Algebraic Expression 8 times a number The product of 12 and a number Double a number (meaning “2 times”) The quotient of –6 and a number A number divided by 10 15 subtracted from 4 times a number The result is

Translate sentences into equations. If 5 times a number is added to 11, the result is 26. Find the number. Example Let x represent the unknown number. The number is 3.

Translate sentences into equations. (continued) Example Check We see that 5 • 3 + 11 = 15 + 11 = 26.

Solve application problems with one unknown quantity.

Solve application problems with one unknown quantity. Example Heather put some money aside in an envelope for small household expenses. Yesterday she took out $20 for groceries. Today a friend paid back a loan and Heather put the $34 in the envelope. Now she has $43 in the envelope. How much was in the envelope at the start? Step 1 Read the problem: Unknown: amount of money in the envelope at the start Known: took out $20; put in $34; ended up with $43

Solve application problems with one unknown quantity. Example (continued) Step 2(a) Assign a variable: Let m represent the money at the start. Step 3 Write an equation:

Solve application problems with one unknown quantity. Example (continued) Step 4 Solve the equation:

Solve application problems with one unknown quantity. (continued) Example Step 5 State the answer: There was $29 in the envelope. Step 6 Check the answer: Started with $29 in the envelope Took out $20, so $29 – $20 = $9 in the envelope Put in $34, so $9 + $34 = $43 Now has $43

Solve application problems with one unknown quantity. Example Michael has completed 5 less than three times as many lab experiments as David. If Michael has completed 13 experiments, how many experiments has David completed? Step 1 Read the problem: Unknown: number of experiments David did Known: Michael did 5 less than 3 times the number David did; Michael did 13.

Solve application problems with one unknown quantity. Example (continued) Step 2(a) Assign a variable: Let n represent the number of experiments David did. Step 3 Write an equation:

Solve application problems with one unknown quantity. Example (continued) Step 4 Solve the equation:

Solve application problems with one unknown quantity. Example (continued) Step 5 State the answer: David did 6 experiments. Step 6 Check the answer: 3 times David’s number 3 • 6 = 18 Less 5 18 – 5 = 13 Michael did 13