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Solving Age and Rate Problems with Equations

This practice session focuses on solving various algebraic equations related to age differences and rates. Students will determine the birth year of a sibling based on age differences, calculate time needed to bake multiple cakes, and solve straightforward equations (e.g., x - 3 = -7). Additionally, algebraic expressions involving variables will be formed to solve real-world problems, including estimating the capacity of an elevator and understanding how long natural processes, like tree carbon absorption, take over time. Ideal for reinforcing algebraic concepts.

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Solving Age and Rate Problems with Equations

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  1. Practice 4-1 through 4-4

  2. Do Now • Mrs. Tilli was born in 1984. She is 14 years older than her little brother Chase. Write and solve an equation to find the year that Chase was born. • Mrs. Cieri can make 2 cakes in an hour. How long will it take her to make 24 cakes? • Solve: x−3= -7 • B+3=10 • -3h=27 • g/5=4

  3. Practice 4-1 • 29 • 30 • 4 • 14 • 24 • 56 • 11 • 28 • 112 • 2n+3 • 16 more than n • 3.2 times n • 25.6 n less than • N divided by 24 • 45 divided by n • 15.4 n less than • M+12 • 6f • A-25 • s/10 • 21a. 5m • 21b. $26.25

  4. Guided Problem Solving 4-1 • Write an algebraic expression for the approximate number of names in p pages of the directory. • A mathematical phrase with at least one variable • The number of pages in the directory • 11 names • 110 names • 440 names • 440 names • 440p names • 440p names • 440; 880; 1,320; yes • 48p

  5. Practice 4-2 • 30 • 99 • 29.6 • 57 • T=5 • W=8 • P=7 • A=13 • H=24 • G=128 • Y=39 • D=16 • W=25 • T=4 • Y=10.64 • X=104.97 • 210+x=520; about 300 cans • $25.30x=$227.70; about 10 bolts of fabric • $.79x=$11.85; 15 balloons

  6. Guided Problem Solving 4-2 • 2,000 lb; 55-lb boxes • Write an equation to estimate the number of boxes you can safely place on the elevator at one time. • The number of boxes • 2,000 lbs • 55 lb • 55x=2,000 • 36 boxes • Yes; 36 boxes × 55 lb/box=1,980 lb • 65x=5,000; x is about 77 minutes or 1 hour 17 minutes

  7. Practice 4-4 • 14 • -243 • -28 • -18 • 36 • 48 • -7 • -7 • 16 • -52 • -7 • -126 • -96 • -5 • 4 • 288 • -399 • 1,386 • -4 • -8,918 • -113 • -50 • 15n=240, n=16; 16 flowers • 10,500/n=1,500, n=7; 7 gal

  8. Guided Problem Solving 4-4 • 26 lb; 390 lb • Find the number of years it will take for a tree to absorb 390 lb of carbon dioxide • Multiplication; the number of years times the amount of carbon dioxide a tree absorbs each year equals the total amount of carbon dioxide absorbed. • 26 lb • 26y lb • 26y=390 • Y=15 • 15 years • 26y=390; 26 ×15=390; 390=390 • 8x=1000; x=125 days

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