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Distribution in Percentage Equations and Word Problems

Distribution in Percentage Equations and Word Problems. 3-5-3. Rate times Amount. Example. One item is 35% off. Another item that costs $5 less than the original price of the first is 40% off. 0.35 times the amount 0.35(x) 0.40 times its amount 0.40(x-5)

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Distribution in Percentage Equations and Word Problems

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  1. Distribution in Percentage Equations and Word Problems 3-5-3

  2. Rate times Amount

  3. Example • One item is 35% off. • Another item that costs $5 less than the original price of the first is 40% off. • 0.35 times the amount 0.35(x) • 0.40 times its amount 0.40(x-5) • Add to get total 0.35(x)+0.04(x-5)

  4. Word Problem • Write “Let x be _________” • Work each phrase of the problem. • Read the problem often enough to understand what is happening and what is asked.

  5. Examples: • One item is $4 less than three times another. The items total $75. How much are each of the two items? • One item is three times as much as $4 less another item. The total is $75. How much are each of the two items?

  6. Examples: • One item is $4 less than three times another. The items total $75. How much are each of the two items? • Let x be one item. • 3x-4 is the other item • The total is x + 3x-4 • The equation is x+3x-4=75 • 4x-4=75 • 4x=71 • x=$17.75 • The other item is $49.25

  7. Examples: • One item is three times as much as $4 less another item. The total is $75. How much are each of the two items? • Let x be one item. • 3(x-4) is the other. • x+3(x-4)=75 • x+3x-12=75 4x-12=75 • 4x=87 x=$21.75 53.25 is the other

  8. Draw a Picture • If you can draw a picture and label the parts. • A rectangle is twice as long as five inches less than the width. The perimeter is 500 in. • One side is w • The other is 2(w-5) • P=2w+2(2(w-5))=500 2(w-5) w

  9. Stamps Money Tickets and Solutions • Rate times amount + rate times amount • Joan has 3 more dimes than quarters. She has twice as many nickels as quarters. She has $2.10 . How many of each coin does she have? • Let x be quarters. • x+3 is dimes • 2x is nickels

  10. Rate (or worth) times amount • Rate times amt. +rate times amt.+ rate times amt. • 0.25(x) +0.10(x+3) + 0.05(2x) = 2.10 • 0.25x +0.10x + 0.3 + 0.1x = 2.10 • 0.45x+0.3 = 2.1 • 0.45x=1.8 • x=4 quarters 7 dimes 8 nickels

  11. Solutions • Rate times amount + rate times amt= total • Cashews are added to a nut mixture with 25% cashews to make 12 lbs of a 40% cashew mix. How much of each plain cashews and 25% mix is needed? • Let x be straight cashews. (100%) • 12-x is need to make 12 lbs total. • 1.00x+0.25(12-x)=0.40(12)

  12. Solutions • Rate times amount + rate times amt= total • A 20% alcohol solution is to be added to water to make 20 liters of 5% solution. • Let x be the alcohol solution • 20-x is the water (0%) • 0.20x+0.0(20-x)=0.05(20)

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