12. word problems linear

8/6/2019 12. Word Problems Linear

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Algebraic expression

The sum of a number and 4

7 more than a number

Anumber plus 6

Anumber increased by 10

8 added to a number

n + 4

n + 7

n + 6

n + 10

n + 8


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14 minus a number

12 less than a number

Anumberdecreased by 10

Thediff. bet. a number and 2

5 subtracted from a number

14 n

n 12

n 10

n 2

n 5


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14 times a number

The product of 4 & a number

of a number

Twice a number

Anumbermultiplied by 12

14n

4n

()n

2n

12n


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Quotient of 6 and a number

Quotient of a number and 6

Anumberdivided by 9

Theratio of a number and 4

6/n

n/6

n/9

n/4


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Algebraic expression4 more than 3 times a number

5 less than twice a number

Three times the sum of anumber and 2

2 more than the quotient of anumber and 12

7 times the difference of 6 and anumber

3n + 4

2n 5

3(a + 2)

n/12 + 2

7(6 n)


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Note: is usually means is equal to

4 more than 3 times anumberis 10

5 less than twice a numberis 25

7 times the difference of 6and a numberis 21

3n + 4 = 10

2n 5 = 25

7(6 n)= 21


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Note: is usually means is equal to

Twice a numberis 12 lessthan the number

Anumber divided by 3 is 6less than the number

Anumber decreased by 10 is5 less than twice a number

2n = n 12

n/3 = n 6

n 10 = 2n 5


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Note: Consecutive Integers are represented by

n, n + 1, n + 2, n + 3,

1. The sum of 4 consecutive integers is 46. Find thelargest of them.

1st 2nd 3rd 4th

n + (n + 1) + (n + 2) + (n + 3)= 46

n = 10

The integers are 10, 11, 12 and 13

Therefore, the largest of them is 13.


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Note: an even number is denoted by 2n

2. The sum of 3 consecutiveeven numbers is 12. Whatare the numbers?

1st 2nd 3rd

2n + (2n + 2) + (2n + 4)= 12

n = 1

1st number is 2(1) = 2

Therefore, even integers are 2, 4 and 6


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Note: an odd number is denoted by 2n + 1

3. The sum of 2 consecutive 0dd numbers is 32. What arethe numbers?

1st 2nd

(2n + 1) + (2n + 3)= 32

n = 7

1st number is 2(7) + 1 = 15

Therefore, odd integers are 15 and 17.


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Number Problem

4. The sum of 3 consecutiveeven integers is 14 more thantwice the smallest. Find the largest.

2n + (2n+2) + (2n+4) = 2(2n) + 14

5. There are three consecutiveodd integers. Their sum is21 less than 4 times the largest. Find the numbers.

(2n+1) + (2n+3) + (2n+5) = 4(2n+5) - 21


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Investment Problem

1. How much does Oz need to place at an investmentthat pays 4% to earn P10,000 in one year?

Interest = Principal x Interest Rate x term

10,000 = x(4%)(1)

x = 250,000

Therefore, he needs to invest P250,000.


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Investment Problem

2. Kyle invested P20,000 in a savings account that earns 10%.How much should she invest at another savingswith arate of 5% so that her total earnings is P3,500 in one year?

InterestA+ Interest B = Total interest

20,000(10%) + x(5%) = 3,500

x = 30,000

Therefore, she needs to invest P30,000 in the 5% savings.


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Investment Problem

3. Maryhas P50,000 to invest in 2 separate investments,one at 5% and the other at 6%. How much should sheinvest in each to earn P2,700 in one year?

InterestA+ Interest B = Total Interest

x(5%) + (50,000 x)(6%) = 2,700

x = 30,000

Therefore, P30,000 at 5% and P20,000 at 6%.


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Investment Problem

4. Nikko plans to earn exactly P4,000 in one year out of twoinvestments, one at 4% and the other at 8%. Ifhehas aP80,000 to invest, how much should he place in each?


x(4%) + (80,000 x)(8%) = 4,000

x = 60,000

Therefore, P60,000 at 4% and P20,000 at 8%.


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5. Julia invested a total amount of P100,000 in two banksAand B that pays 7% interest and 10% respectively. Howmuch total earningswill sheget if she invested ofher

money in 7% and therest at 10%?

(1/4)(100,000) = 25,000


25,000(7%) + 75,000(10%) = x

x = P9,250

Investment Problem


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ixture Problem

1. Amixture ofrice and corn is to be sold at P32 per kilo.How many kilos ofrice that costs P30/k must be mixedwith 25k of corn that costs P36/k to achievehis goal?

CostA+ Cost B = Cost (A+ B)

30(25) + 36(x) = 32(25 + x)

x = 12.5

Therefore, he needs 12.5k ofrice in the mixture.


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2. How manygrams of puregold must be added to 100grams, 50% pure, to make a mixturewhich is 75%pure?

% of MixtureA+ % of MixtureB = % of Mixture (A+ B)

100% (x) + 50% (100) = 75% (x + 100)

x = 100 grams

Therefore,we need 100 grams of puregold.

ixture Problem


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3.A10-liter brine solution is 25% pure salt. How muchwatermust be added to produce a solutionwhich is20% salt?

% of MixtureA+ % of MixtureB = % of Mixture (A+ B)

25% (10) + 0% (x) = 20% (10 + x)

x = 2.5 liters

Therefore,we need 2.5 liters ofwater.

ixture Problem


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4. How muchwater must be added to 70 liters of 90%alcohol to create a 60% alcohol solution?

5.Astorekeeperhas candies that sells for P60 and P90per kilogram. How many kilograms ofeach must be

mixed together to make 100 kilograms of candy thatwould be sold at P72 per kilogram?

ixture Problem

12. word problems linear

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