# Solving Equations help.?

1. The product of two consecutive positive integers is 11 more than their sum. Find the integers.

2. Solve.

v^2 = 18 - 3v

3. Solve by the substitution method.

15x - 20y = -1

15y = 2 + 5x

3. Solve by the elimination method.

8x - y = 68

x + 3y = 21

4. Solve by the substitution method.

15x - 10y = -5

15y = 4 + 5x

5. Solve the system of equations by the substitution.

0.06x - 0.01y = 0.6

0.22x + 0.13y = 12.2

6. A motel clerk counts his \$1 and \$10 bills at the end of a day. He finds that he has a total of 59 bills having a combined monetary value of \$239. Find the number of bills of each denomination that he has.

the clerk has ____ ones and ___ tens.

Relevance
• 9 years ago

1)

the first integer is = x

the second integer is ( x + 1 )

the product as x (x + 1)

their sum x + (x + 1) -----> 2x + 1

consecutive positive integers is 11 more than their sum

x (x + 1) = 11 + 2x + 1

x^2 + x = 12 + 2x

x^2 + x - 12 - 2x = 0

x^2 - x - 12 = 0

(x - 4)(x + 3) = 0 =====> x = -3 & 4

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2)

v^2 = 18 - 3v

v^2 + 3v - 18 = 0

(v + 6)(v - 3) = 0 =====> v = -6 & 3

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3)

15x - 20y = -1 ====> 15x = 20y - 1 =====> x = (20/15) y - (1/15) ===> x = (4/3) y - (1/15)

substitute it into :

15y = 2 + 5 * ( (4/3) y - (1/15) )

15y = 2 + (20/3) y - (1/3)

15y - (20/3) y = (5/3)

(25/3) y = (5/3)

25 y = 5

y = 1/5

when y = 1/5

x = (4/3) (1/5) - (1/15)

x = (4/15) - (1/15)

x = (3/15)

x = 1/5

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3)

8x - y = 68

x + 3y = 21 ===> * -8

8x - y = 68

+

-8x - 24y = -168

-----------------------

0 - 25y = -100 ======> y = 4

when y = 4

8x - 4 = 68

8x = 68 + 4

8x = 72

x = 9

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4)

15x - 10y = -5 ====> 15x = 10y - 5 ====> x = (10/15) y - (5/15) ====> x = (2/3) y - (1/3)

substitute in:

15y = 4 + 5 * ( (2/3) y - (1/3) )

15y = 4 + (10/3) y - (5/3)

15y - (10/3) y = (7/3)

(35/3) y = (7/3)

35 y = 7

y = 1/5

when y = 1/5

x = (2/3) (1/5) - (1/3)

x = (2/15) - (1/3)

x = -1/5

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5)

(6/100) x - (1/100)y = 6/10

(22/100)x + (13/100)y = 122/10

6x - y = 60 =====> * 13

22x + 13y = 1220

78x - 13y = 780

+

22x + 13y = 1220

-----------------------

100x + 0 = 2000 ====> x = 20

when x = 20

6*20 - y = 60

120 - 60 = y

60 = y

============

6)

\$1 ------- call it -----> x

\$10------ call it -----> y

has a total of 59 bills -----> x + y = 59

combined monetary value of \$239

1x + 10y = 239

x + y = 59

- <-- minus

x + 10y = 239

--------------------

0 - 9y = -180 =====> y = 20

when y = 20

x + 20 = 59

x = 59 - 20

x = 39

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