Question

A concession stand sold ice cream cones, salted pretzels, and tacos at a basketball game. Ice cream cones were sold for $3.00, salted pretzels were sold for $2.50, and tacos were sold for $2.00. The total number of ice cream cones, salted pretzels, and tacos sold was 140, and the total amount of money from these items was $359.50. If $70.00 was made just from selling tacos, how many salted pretzels were sold?

Answer 1

51 salted pretzels were sold.

Explanation:

Step 1: Write the data

Number of Ice cream cones sold: x

Cost of ice cream cones sold: 3x

Number of Salted pretzels sold: y

Cost of salted pretzels sold: 2.5y

Number of tacos sold: z

Cost of tacos sold: 2z

Step 1: Make equation 1

Total money made: $359.5

Money made from tacos: $70

Money made from ice cream cones and salted pretzels: 359.5-70 = $289.5

Equation 1:

3x + 2.5y = 289.5

Step 3: Make equation 2

Cost per tacos: $2

Total number of tacos sold: z

Money made from total tacos: $70

2z = 70

z = 35 tacos were sold

Total number of ice cream cones and salted pretzels sold: 140-35 = 105

Equation 2:

x + y = 105

Step 4: Find the unknown value by substitution

3x + 2.5y = 289.5

x + y = 105

Find x in terms of y from equation 2

x + y = 105

x = 105 - y

Substitute x in equation 1

3x + 2.5y = 289.5

3(105-y) + 2.5y = 289.5

315 - 3y + 2.5y = 289.5

0.5y = 25.5

y = 51

y represents the number of salted pretzels sold. Therefore, 51 salted pretzels were sold.