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

$y = 50 - x$

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