Chapter ISG, Problem 2.1.1.4P

a.

To determine

To write and solve an equation

Answer to Problem 2.1.1.4P

  $3x=21$

She invited 7 school friends

Explanation of Solution

Given information:

Barbara invited 2 times as many friends from her swimming club as school friends.

Total 21 friends came.

Calculation:

Let the number of school friends be x,

So, number of college friends=2x

Total number of friends came is 21

Now, according to question,

  $x+2x=21$

Simplifying,

  $3x=21$

This is the equation

Solving,

x=7

Hence, she invited 7 school friends

b.

To determine

To write and solve the equation

Answer to Problem 2.1.1.4P

Equation: $\frac{87}{100}\times x=174$

200 players signed up for the league

Explanation of Solution

Given information:

13% of players who signed dropped of the soccer team.

Total 174 players finished the season.

Calculation:

Let total players be x,

13% of total players were dropped out. Means 100-13= 87 player finish the league,

Hence,

  $\frac{87}{100}\times x=174$

This is the equation

Solving,

  $87x=174\times 100$

So,

  $x=\frac{174\times 100}{87}$

Hence, x=200

200 players signed up for the league

c.

To determine

To write and solve an equation

Answer to Problem 2.1.1.4P

Equation: $12(x+1)+10(x)=188$

Number of geometry is 8.

Explanation of Solution

Given information:

Mr. Rhoades ordered 188 books.

Algebra books were packed in boxes of 12.

Geometry books were packed in boxes of 10l

He ordered one more box of algebra books than geometry box.

Calculation:

Let the number of geometry book box be x,

According to question,

Algebra boxes = x+1

Now,

  $12(x+1)+10(x)=188$

This is the equation

Solving,

  $12x+12+10x=188$

So,

  $22x=188-12$

Dividing by 22,

  $x=\frac{176}{22}$

Hence, number of geometry is 8.