Q: If $$x is $$the number of cups sold at $$\2$ and y$ is the number of cups sold at $$\$$3$$, which system of equations correctly models the lemonade problem?

$$\begin{cases} x + y = 50 \\ 2x + 3y = 124 \end{cases}$$

Question 1

Bill earned 3 times as much as Jim in one weekend. Tom earned $$5 more than Jim. If together they earned 90$$, how much did each person earn?

Accepted Answer

$$\15$ for Jim, $$\$$45$$ for Bill, $$\20$ for Tom

Question 2

The lengths of the sides of a triangle are represented by three consecutive integers. If the perimeter of the triangle is $$18$$ feet, what are the lengths of its sides?

Accepted Answer

$$5 ft$$, $$6 ft$$, $$7 ft$$

Question 3

A child is selling lemonade. She started by charging $$\2$ per cup, but later increased the price to $$\$$3$$ per cup. She sold all $$50$$ cups and earned $$\124$. How many cups did she sell at $$\$$2$$ each?

Accepted Answer

$$24$$ cups

Question 4

If $$x is $$the number of cups sold at $$\2$ and y$ is the number of cups sold at $$\$$3$$, which system of equations correctly models the lemonade problem?

Accepted Answer

$$\begin{cases} x + y = 50 \ 2x + 3y = 124 \end{cases}$$

Question 5

Suppose the lengths of the sides of a triangle are $$x$$, $$x+1$$, and $$x+2. If $$the perimeter is $$18$$ feet, what is the value of $$x$$?

Accepted Answer

$$x = 5$$

Question 6

If Jim earned $$x$$ dollars, Bill earned $$3x$$ dollars, and Tom earned $$x+5$$ dollars, and together they earned $$90$$, what is the value of $$x$$?

Accepted Answer

$$x = 15$$

Question 7

A child sold $$x$$ cups of lemonade at $$\2$ each and y$ cups at $$\$$3$$ each, selling a total of $$50$$ cups and earning $$\124$. What is the value of y$?

Accepted Answer

$$26$$

Question 8

If the sides of a triangle are $$x$$, $$x+1$$, and $$x+2$$, and the perimeter is $$18$$, which equation should you solve to find $$x$$?

Accepted Answer

$$x + (x+1) + (x+2) = 18$$

Question 9

If Bill earned $$3$$ times as much as Jim, and Tom earned $$5$$ more than Jim, which of the following expressions represents the total amount earned by all three?

Accepted Answer

$$x + 3x + (x+5)$$

Question 10

A child sold $$x$$ cups of lemonade at $$\2$ each and y$ cups at $$\$$3$$ each, with $$x + y = 50$$ and $$2x + 3y = 124. $$What is the value of $$x$$?

Accepted Answer

$$24$$

Question 11

If the sides of a triangle are $$5 ft$$, $$6 ft$$, and $$7 ft$$, what is the perimeter?

Accepted Answer

$$18 ft$$

Question 12

If Jim earned $$x$$ dollars, Bill earned $$3x$$ dollars, and Tom earned $$x+5$$ dollars, and together they earned $$90$$, what equation represents this situation?

Accepted Answer

$$x + 3x + (x+5) = 90$$

Question 13

A child sold $$x$$ cups of lemonade at $$\2$ each and y$ cups at $$\$$3$$ each, selling a total of $$50$$ cups and earning $$\124$. Which of the following is an expression for the number of cups sold at $$\$$3$$?

Accepted Answer

$$y = 50 - x$$

College Algebra: Word Problems Involving Linear Equations and Integer Applications

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