Exploring Constants, Variables, and Solution Reasonableness

A store sells apples for $2 each. If you buy x apples, what is the total cost? Identify the constant and variable in this problem.

• Total cost = x + 2; Constant = x; Variable = 2.

• Total cost = 2 + x; Constant = 2; Variable = total cost.

• Total cost = 2 * 2; Constant = x; Variable = 4.

• Total cost = 2 * x; Constant = 2; Variable = x.

Maria has a savings account with a constant balance of $500. She saves $50 each month. Write an equation to represent her savings after m months. What are the constant and variable?

• S = 500 + 50m; constant: 500, variable: m

• S = 500 - 50m; constant: 500, variable: m

• S = 50m; constant: 0, variable: m

• S = 500 + 100m; constant: 500, variable: m

A car travels at a speed of 60 miles per hour. If t represents the time in hours, how far will the car travel? Identify the constant and variable in this scenario.

• 60t kilometers

• 60t miles

• 30t miles

• 120t miles

In a recipe, 3 cups of flour are needed for every 2 cups of sugar. If f represents cups of flour and s represents cups of sugar, write an equation. What are the constants and variables?

• 4f = 5s

• 2f + 3s = 0

• f = 1.5s

• 2f = 3s

A gardener plants x flowers in a row. Each flower needs 2 feet of space. Write an expression for the total space needed. Identify the constant and variable.

• 2x-2

• 2x+1

• x+2

• 2x

A book costs $15. If you buy b books, what is the total cost? Identify the constant and variable in this problem and check if buying 3 books is reasonable.

• The total cost for 3 books is $15.

• The total cost for 3 books is $60.

• The total cost for 3 books is $30.

• The total cost for 3 books is $45.

A train leaves the station every 30 minutes. If h represents the number of hours since the first train, how many trains have left? Identify the constant and variable and check if 5 hours is reasonable.

• 8

• 12

• 15

• 10

A swimming pool is filled with water at a rate of 10 gallons per minute. If t represents time in minutes, how much water is in the pool after t minutes? Identify the constant and variable.

• 5t gallons

• 15t gallons

• 10t + 5 gallons

• 10t gallons

A pizza has 8 slices. If s represents the number of slices eaten, how many slices are left? Write an equation and identify the constant and variable. Is it reasonable to say 10 slices are left?

• No, it is not reasonable to say 10 slices are left.

• The equation is s + 10 = 8.

• There are 5 slices left.

• It is reasonable to say 10 slices are left.

A factory produces 100 toys every hour. If h represents the number of hours, how many toys are produced? Identify the constant and variable and check if producing 300 toys in 2 hours is reasonable.

• The constant is the number of toys produced per hour, which is 200.

• No, producing 300 toys in 2 hours is not reasonable.

• Yes, producing 300 toys in 2 hours is reasonable.

• The factory produces 200 toys in 2 hours.