3 Use the elimination method to solve this problem A snack o

3. Use the elimination method to solve this problem: A snack of 16 peanuts and 5 cashews contains 135 calories. Another snack of 20 peanuts and 25 cashews contains 405 calories. How many calories are in each peanut and each cashew? Page b. Check your answer. Given the following set of numbers, 11,2,2,3,4, 4, 4, 5, 6,8 a. What is the Mean? b. What is the Median? c. What is the Mode? d. What is the Range?

Solution

3)

let number of calories in each peanut =x ,in each cashewnut =y

equations representing given information are 16x+5y =135,20x+25y =405

multiply first equation with 5

5*(16x+5y =135) => 80x+25y =675

now

(80x+25y) -(20x+25y)=675-405

=>80x+25y -20x-25y =270

=>60x=270

=>x=270_/60

=>x=4.5

16x+5y =135, x=4.5

=>(16*4.5)+5y =135

=>72+5y=135

=>5y=135-72

=>5y=63

=>y=63_/5

=>y =12.6

each peanut has 4.5 calories ,each cashewnut has 12.6 calories

b)

Check:

(16*4.5)+(5*12.6) =72+63=135

(20*4.5)+(25*12.6)=90+315 =405

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4)if numbers are 1,1,2,2,3,4,4,4,5,6,8

mean =(1+1+2+2+3+4+4+4+5+6+8)_/11

mean =40_/11

median =4 (is the middle number in sequence)

mode =4 (is the most repeated number)

minimum =1, maximum =8

range =8-1

range =7

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