Question

write equations from verbal descriptions

1. (model with mathematics) the area of a floor in square yards is one - ninth the area of the floor in square feet. write the equation representing ( y ), the area in square yards, to ( f ), the area in square feet.
2. an object’s height is measured in centimeters and inches. write an equation that relates the number of centimeters ( c ) to the number of inches ( i ). determine the height in centimeters of a chair that is 32 inches tall.
3. (model with mathematics) michael practiced his harmonica 3 times as long as timothy did. michael practiced for 126 minutes. write an equation that represents the relationship between the amount of time timothy practiced ( x ) and the amount of time michael practiced.
4. caleb has read 17 more books than his friend liana. write an equation that represents the relationship between ( n ), the number of books caleb has read, and ( p ), the number of books liana has read.

(model with mathematics) for problems 5 - 10, write an equation for each description.

1. felix sold 35 fewer raffle tickets than helene. how many tickets ( f ) did felix sell if helene sold ( m ) tickets?
2. sloane works ( 7\frac{1}{2} ) hours each day. how many hours ( h ) does sloane work in ( d ) days?
3. a grocery store charges $2.49 per pound for organic apples. what is the cost ( c ), in dollars, of ( p ) pounds of organic apples?
4. paula used ( 1\frac{3}{4} ) cups of flour for a recipe. how many cups ( y ) of flour did paula have if she had ( x ) cups before making the recipe?
5. each crate holds 135 avocados. how many avocados ( a ) are in ( c ) crates?
6. every delivery order from a pizzeria has a delivery charge of $1.50. how many dollars ( b ) is the total bill for a delivery of one pizza if the pizza costs ( p ) dollars?

Explanation:

Let's solve each problem one by one:

Problem 2

Step 1: Recall the conversion factor

We know that 1 inch is equal to 2.54 centimeters. So, to relate centimeters \( c \) to inches \( i \), we can use the formula \( c = 2.54i \).

Step 2: Find the height in centimeters for a 32 - inch chair

Substitute \( i = 32 \) into the equation \( c = 2.54i \).
\( c=2.54\times32 = 81.28 \)

Problem 3

Step 1: Define the relationship

Michael practiced 3 times as long as Timothy. Let \( x \) be the time Timothy practiced and \( y \) be the time Michael practiced. Then the equation is \( y = 3x \). We know that \( y = 126 \) minutes.

Step 2: (If we were to find \( x \), but the problem only asks for the equation)

The equation representing the relationship is \( 126=3x \) (or \( y = 3x \) with \( y = 126 \))

Problem 4

Step 1: Define the relationship

Caleb has read 17 more books than Liana. Let \( n \) be the number of books Caleb has read and \( p \) be the number of books Liana has read. Then the equation is \( n=p + 17 \)

Problem 5

Step 1: Define the relationship

Felix sold 35 fewer raffle tickets than Helene. Let \( F \) be the number of tickets Felix sold and \( H \) be the number of tickets Helene sold. Then the equation is \( F=H - 35 \)

Problem 6

Step 1: Define the relationship

Sloane works \( 7\frac{1}{2}=\frac{15}{2} \) hours each day. Let \( h \) be the total hours worked in \( d \) days. The total hours worked is the number of days times the hours per day. So the equation is \( h=\frac{15}{2}d \)

Problem 7

Step 1: Define the relationship

The grocery store charges $2.49 per pound for organic apples. Let \( c \) be the cost in dollars and \( p \) be the number of pounds. The cost is the price per pound times the number of pounds. So the equation is \( c = 2.49p \)

Problem 8

Step 1: Define the relationship

Paula used \( 1\frac{3}{4}=\frac{7}{4} \) cups of flour for a recipe. Let \( x \) be the number of cups she had before and \( y \) be the number of cups she has left. Then the equation is \( y=x-\frac{7}{4} \)

Problem 9

Step 1: Define the relationship

Each crate holds 135 avocados. Let \( a \) be the number of avocados and \( c \) be the number of crates. The number of avocados is the number of crates times the number of avocados per crate. So the equation is \( a = 135c \)

Problem 10

Step 1: Define the relationship

The delivery charge is $1.50 and the pizza costs \( p \) dollars. Let \( b \) be the total bill. The total bill is the cost of the pizza plus the delivery charge. So the equation is \( b=p + 1.50 \)

Answer:

s:

1. Equation: \( \boldsymbol{c = 2.54i} \), Height in centimeters: \( \boldsymbol{81.28} \)
2. Equation: \( \boldsymbol{y = 3x} \) (or \( \boldsymbol{126=3x} \))
3. Equation: \( \boldsymbol{n=p + 17} \)
4. Equation: \( \boldsymbol{F=H - 35} \)
5. Equation: \( \boldsymbol{h=\frac{15}{2}d} \) (or \( \boldsymbol{h = 7.5d} \))
6. Equation: \( \boldsymbol{c = 2.49p} \)
7. Equation: \( \boldsymbol{y=x-\frac{7}{4}} \) (or \( \boldsymbol{y=x - 1.75} \))
8. Equation: \( \boldsymbol{a = 135c} \)
9. Equation: \( \boldsymbol{b=p + 1.50} \)