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

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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 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)

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.

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?

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

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

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 w 2(w-5)

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

Rate (or worth) times amount Rate times amt. +rate times amt.+ rate times amt. 0.25(x) +0.10(x+3) (2x) = x +0.10x x = x+0.3 = x=1.8 x=4 quarters 7 dimes 8 nickels

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)

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)