Write a system of equations to describe the situation below, solve using any method, and fill in the blanks. Lillian went to play miniature golf on Monday, when it cost $12 to rent the club and ball, plus $2 per game. Janelle went Thursday, paying $5 per game, plus rental fees of $3. By coincidence, they played the same number of games for the same total cost. How many games did each one play? How much did each one spend? Lillian and Janelle each played _____ games and spent $_____.

Question

Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.  Lillian went to play miniature golf on Monday, when it cost $12 to rent the club and ball, plus $2 per game. Janelle went Thursday, paying $5 per game, plus rental fees of $3. By coincidence, they played the same number of games for the same total cost. How many games did each one play? How much did each one spend?   Lillian and Janelle each played _____ games and spent $_____.

Bytelearn · Accepted Answer

Forming First Equation: Let's denote the number of games both Lillian and Janelle played as 'g'. Lillian's total cost is the sum of the rental fee and the cost per game, which is $12 + $2g. Janelle's total cost is the sum of her rental fee and the cost per game, which is $3 + $5g. Since they both spent the same total cost, we can set these two expressions equal to each other to form our first equation.Setting up Equations: The first equation is Lillian's total cost: $12 + $2g. The second equation is Janelle's total cost: $3 + $5g. Since both costs are equal, we can write the equation as $12 + $2g = $3 + $5g.Solving for 'g': To solve for 'g', we need to get all the terms with 'g' on one side and the constants on the other. We can do this by subtracting $2g from both sides and subtracting $3 from both sides to isolate 'g'. $12 + $2g - $2g = $3 + $5g - $2g $12 = $3 + $3g $12 - $3 = $3g $9 = $3gCalculating Number of Games: Now we divide both sides by $3 to solve for 'g'. $9 / $3 = $3g / $3 $3 = g So, Lillian and Janelle each played 3 games.Calculating Total Cost: Now that we know the number of games, we can calculate the total cost for each person. For Lillian, the total cost is $12 + $2g, and for Janelle, the total cost is $3 + $5g. We substitute 'g' with 3. Lillian's total cost: $12 + $2(3) = $12 + $6 = $18 Janelle's total cost: $3 + $5(3) = $3 + $15 = $18

Full solution

More problems from Solve a system of equations using any method: word problems

Related topics