Chapter ISG, Problem 6.2.6P

a.

To determine

To write and solve system of equation

Answer to Problem 6.2.6P

Explanation of Solution

Given information:

4 notebooks and 5 pens bought

7 notebooks and 3 pens bought

Calculation:

Let cost of 1 notebook be x and cost of 1 pen be y

According to question

  $4x+5y=15$   -(1)

  $7x+3y=20.50$   -(2)

Taking (1)

  $4x+5y=15$

Solving,

  $4x=15-5y$

Dividing by 4,

  $x=\frac{15-5y}{4}$

(-3)

Put value of x in (2)

  $7(\frac{15-5y}{4})+3y=20.50$

Solving,

  $105-35y+12y=20.50\times 4$

So,$-23y=-23$

Dividing equation by -23,

  $y=1$

Put y in (3)

  $x=\frac{15-5(1)}{4}$

Solving,

  $x=2.5$

Hence, cost of pen is $1 and, cost of notebook is $2.5

b.

To determine

To verify Susan’s shopping

Answer to Problem 6.2.6P

Yes, S has enough money.

Explanation of Solution

Given information:

Amount S has=$17

Number of notebook wanted to be bought= 5

Number of pen wanted to be bought= 4

Calculation:

Cost of pen =$1

Cost of notebook=$2.5

According to question,

Equation= $5x+4y$

Put value of x and y,

Equation= $5(2.5)+4(1)$

Solving,

  = $12.5+4$

Total cost of buying is $16.5

And S has $17.

Yes, S can buy the stuff