A large pizza at one pizza shop costs $14.50, and each topping costs $2.50. A large pizza at another pizza shop costs $17.00, and each topping costs $1.60. The system of equations graphed on the grid represents this situation.
Which statement is true about the cost of a large pizza at the two pizza shops?
The cost of a large pizza with 21 toppings is about the same at the two pizza shops.
The cost of large pizza with 3 toppings is about the same at the two pizza shops.
The cost of large pizza with 17 toppings is about the same at the two pizza shops.
The cost of large pizza with 8 toppings is about the same at two pizza shops.
To determine which statement is true, we need to find the cost of a large pizza at each shop with the given number of toppings.
For the first pizza shop, each topping costs $2.50. So for 21 toppings, the cost of the toppings would be 21 * $2.50 = $52.50. Therefore, the total cost of a large pizza with 21 toppings at this shop would be $14.50 + $52.50 = $67.
For the second pizza shop, each topping costs $1.60. So for 21 toppings, the cost of the toppings would be 21 * $1.60 = $33.60. Therefore, the total cost of a large pizza with 21 toppings at this shop would be $17 + $33.60 = $50.60.
Since the cost of a large pizza with 21 toppings is not about the same at the two pizza shops, we can eliminate option A.
For the first pizza shop, each topping costs $2.50. So for 3 toppings, the cost of the toppings would be 3 * $2.50 = $7.50. Therefore, the total cost of a large pizza with 3 toppings at this shop would be $14.50 + $7.50 = $22.
For the second pizza shop, each topping costs $1.60. So for 3 toppings, the cost of the toppings would be 3 * $1.60 = $4.80. Therefore, the total cost of a large pizza with 3 toppings at this shop would be $17 + $4.80 = $21.80.
The cost of a large pizza with 3 toppings is about the same at the two pizza shops. Therefore, option B is correct.
For the first pizza shop, each topping costs $2.50. So for 17 toppings, the cost of the toppings would be 17 * $2.50 = $42.50. Therefore, the total cost of a large pizza with 17 toppings at this shop would be $14.50 + $42.50 = $57.
For the second pizza shop, each topping costs $1.60. So for 17 toppings, the cost of the toppings would be 17 * $1.60 = $27.20. Therefore, the total cost of a large pizza with 17 toppings at this shop would be $17 + $27.20 = $44.20.
The cost of a large pizza with 17 toppings is not about the same at the two pizza shops. Therefore, we can eliminate option C.
For the first pizza shop, each topping costs $2.50. So for 8 toppings, the cost of the toppings would be 8 * $2.50 = $20. Therefore, the total cost of a large pizza with 8 toppings at this shop would be $14.50 + $20 = $34.50.
For the second pizza shop, each topping costs $1.60. So for 8 toppings, the cost of the toppings would be 8 * $1.60 = $12.80. Therefore, the total cost of a large pizza with 8 toppings at this shop would be $17 + $12.80 = $29.80.
The cost of a large pizza with 8 toppings is about the same at the two pizza shops. Therefore, option D is also correct.
In conclusion, both option B and option D are true about the cost of a large pizza at the two pizza shops.