EXAMPLE 1 Using a Variable Expression Hot Air Balloons You are riding in a hot air balloon. After traveling 5 miles, the balloon speed changes to 6 miles.

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EXAMPLE 1 Using a Variable Expression Hot Air Balloons You are riding in a hot air balloon. After traveling 5 miles, the balloon speed changes to 6 miles per hour. So, the total distance traveled is original distance + speed time, which is t, where t is the number of hours traveled at 6 mi/h.

EXAMPLE 1 Using a Variable Expression SOLUTION STEP 1 STEP 2 STEP 3 Write hours traveled t. Substitute for t in the expression t. Evaluate to find total distance (1) 5 + 6(2) ANSWER If the balloon travels at 6 miles per hour for 1 hour, you travel a total of 11 miles. After 2 hours you travel a total of 17 miles.

GUIDED PRACTICE for Example 1 What If? Use the information above about hot air balloons. 1.If you travel at 6 miles per hour for 3 hours, what is the total distance? SOLUTION STEP 1 STEP 2 STEP 3 Write hours traveled t. Substitute for t in the expression t. Evaluate to find total distance (3) 23 ANSWER If the balloon travels at 6 miles per hour for 3 hours, you travel a total of 23 miles.

GUIDED PRACTICE for Example 1 2.If you travel at 6 miles per hour for hour, what is the total distance? 1 2 SOLUTION STEP 1 STEP 2 STEP 3 Write hours traveled t. Substitute for t in the expression t. Evaluate to find total distance (0.5) 8 ANSWER If the balloon travels at 6 miles per hour for hour, you travel a total of 8 miles. 1 2

GUIDED PRACTICE for Example 1 3.If you travel at 3 miles per hour for 2 hours, what is the total distance? SOLUTION STEP 1 STEP 2 STEP 3 Write hours traveled t. Substitute for t in the expression t. Evaluate to find total distance (2) 11 ANSWER If the balloon travels at 3 miles per hour for 2 hour, you travel a total of 11 miles.

EXAMPLE 2 Evaluating Variable Expressions Evaluate the expression when x = 8 and y = 2. a. 3x – 5y3(8) – 5(2) = 24 – 10 = 14 = Substitute 8 for x and 2 for y. Multiply. Subtract. 5(8+2) = 50 = Substitute 8 for x and 2 for y. Add. b. 5(x + y) = 5(10) Multiply.

EXAMPLE 3 Translating Verbal Phrases Verbal PhraseVariable Expression The sum of a number and 9 The difference of a number and 21 The product of 6 and a number The quotient of 48 and a number One third of a number n + 9 n – 21 6n6n 48 n 3 1 n

GUIDED PRACTICE for Examples 2 and 3 Evaluate the expression when a = 12 and b = a 5. ab Substitute 12 for a = 9(12) = 108 Substitute 12 for a and 3 for b = (12)(3) = 36 Multiply.

GUIDED PRACTICE for Examples 2 and 3 Evaluate the expression when a = 12 and b = b(a – 6) = 3(12 – 6) Substitute 12 for a and 3 for b = 3(6) Subtract. Multiply. = 18

GUIDED PRACTICE for Examples 2 and 3 Evaluate the expression when a = 12 and b = a6a a – b Substitute 12 for a and 3 for b 6(12) 12 – 3 = – 3 = Multiply = Subtract. = 8 Divide.

GUIDED PRACTICE for Examples 2 and 3 Write the phrase as a variable expression using x. 8. a number increased by times a number Verbal PhraseVariable Expression x x8x

EXAMPLE 4 Writing and Evaluating an Expression Heart Rate a. Use n to write an expression for heart rate in beats per minute. b. After exercising, you count 24 beats in 15 seconds. Find your heart rate. To measure your heart rate, count the number of heartbeats n in 15 seconds. Then multiply by 4 to find your heart rate in beats per minute.

EXAMPLE 4 Writing and Evaluating an Expression SOLUTION a. The phrase multiply by suggests multiplication. So, multiply the number of heart beats n by 4. ANSWER A variable expression for heart rate in beats per minute is 4 n. b. Substitute 24 for n in the expression 4 n to find your heart rate. 4 n = 4(24) = 96 ANSWER Your heart rate is 96 beats per minute.

GUIDED PRACTICE for Example Savings You have $25 saved. You save $4 more per week for n weeks. Write and evaluate an expression for your total savings after 8 weeks. = n = (8) = 57 SOLUTION ANSWER Total saving after 8 weeks is $57