Step: 1

Let number of men be x .

Step: 2

Let number of women be y .

Step: 3

[Linear equation for the number of men and women hired.]

Step: 4

9x + 7y = 6244 --- (2)

[Equation for the daily wages paid.]

Step: 5

[Revise equation 1.]

Step: 6

9x + 7(770 - x ) = 6244

[Substitute y = 770 - x in Equation 2.]

Step: 7

2x + 5390 = 6244

[Combine like terms.]

Step: 8

2x = 854

[Subtract 5390 from each side.]

Step: 9

[Divide each side by 2.]

Step: 10

[Substitute x = 427 in revised Equation 3.]

Step: 11

343 women and 427 men are hired.

Correct Answer is : 427 men, 343 women

Step: 1

Let number of men be x .

Step: 2

Let number of women be y .

Step: 3

[Linear equation for the number of men and women hired.]

Step: 4

10x + 6y = 6432 --- (2)

[Equation for the daily wages paid.]

Step: 5

[Revise equation 1.]

Step: 6

10x + 6(790 - x ) = 6432

[Substitute y = 790 - x in Equation 2.]

Step: 7

4x + 4740 = 6432

[Combine like terms.]

Step: 8

4x = 1692

[Subtract 4740 from each side.]

Step: 9

[Divide each side by 4.]

Step: 10

[Substitute x = 423 in revised Equation 3.]

Step: 11

367 women and 423 men are hired.

Correct Answer is : 423 men, 367 women

Step: 1

Let x be the number of pound of sugar and y be the number of pound of flour bought by Carol.

Step: 2

[As per the question.]

Step: 3

5x - 4y = 23 - - - - - - - - - (2)

[As per the question.]

Step: 4

4x + 4y = 76

[Multiply the first equation by 4.]

Step: 5

9x = 99

[Solve the equations in step 3 and step 4.]

Step: 6

[Divide both sides by 9.]

Step: 7

Step: 8

[Replace x = 11.]

Step: 9

Therefore, Carol bought 11 pound of sugar and 8 pound of flour

Correct Answer is : Sugar: 11, Flour 8

Step: 1

Let the price of the book = $x

Step: 2

Let the price of the pen = $y

Step: 3

5x + y = 79

[First equation from the data.]

Step: 4

[Second equation from the data.]

Step: 5

[Solve the first equation for y .]

Step: 6

[Substitute the values.]

Step: 7

Step: 8

- 79x = 158 - 1264

Step: 9

- 79x = - 1106

[Subtract.]

Step: 10

[Divide throughout by - 79.]

Step: 11

16y = 158 - x = 158 - 14 = 144

[Substitute the values.]

Step: 12

[Divide throughout by 16.]

Step: 13

So, the price of the book is $14 and the price of the pen is $9.

Correct Answer is : $14, $9

Step: 1

Let x be the number of books and y be the number of toys, Paula purchased.

Step: 2

[Express as a linear equation.]

Step: 3

23x + 12y = 839 --- (2)

[Equation for the total cost of the books and toys.]

Step: 4

23x + 12(- x + 47) = 839

[From equation 1, y = - x + 47. Substitute it in equation 2.]

Step: 5

11x + 564 = 839

[Group the like terms.]

Step: 6

11x = 275

[Subtract 564 from the two sides of the equation.]

Step: 7

[Divide throughout by 11.]

Step: 8

[Substitute the values.]

Step: 9

Paula bought 25 books and 22 toys.

Correct Answer is : 25 books and 22 toys

Step: 1

[Total number of candies and cookies = 10.]

Step: 2

Cost of x candies is $x .

[Cost of a candy = $1.]

Step: 3

Cost of y cookies is $0.9y .

[Cost of a cookie = $0.9.]

Step: 4

Cost of 10 candies and cookies is $24, so x + 0.9y = 24

[Total cost = $24.]

Step: 5

Correct Answer is : x + y = 10 and x + 0.9y = 24

Step: 1

[Total number of soaps and shampoo bottles is 28.]

Step: 2

Cost of x soaps = $3x

[Cost of a soap = $3.]

Step: 3

Cost of y shampoo bottles = $10y

[Cost of a shampoo bottle is $10.]

Step: 4

Step: 5

So, the system of equations are x + y = 28 and 3x + 10y = 174.

Correct Answer is : x + y = 28 and 3x + 10y = 174

Step: 1

- x + y = - 2

[Equation 1.]

Step: 2

3x - y = - 4

____________

____________

[Equation 2.]

Step: 3

2x = - 6

[Add Equation 1 and Equation 2.]

Step: 4

So, adding the two equations is a good step to solve the linear system of equations.

Correct Answer is : Adding the two equations.

Step: 1

- x + y = 6

[Equation 1.]

Step: 2

5x - 4y = -12

[Equation 2.]

Step: 3

So, substitute y = 6 + x for y in the second equation is the first step to solve the system of equations.

Correct Answer is : Substitute y = 6 + x for y in the second equation.

Step: 1

Let x be the smaller number and y be the larger number.

Step: 2

11y = 6x + 14 - - - - - - - - - - - (1) and 10x = 4y + 34 - - - - - - - - - - - - -(2)

[As per the question.]

Step: 3

- 24x + 44y = 56

[Multiply equation (1) with 4.]

Step: 4

110x - 44y = 374

[Multiply equation (2) with 11.]

Step: 5

86x = 430

[Add.]

Step: 6

[Divide both sides by 86.]

Step: 7

11y = 6(5) + 14

[Replace x with 5 in equation (1).]

Step: 8

11y = 44

Step: 9

Step: 10

So, the two numbers are 5 and 4.

Correct Answer is : 5, 4

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