1. The Frosty Ice-Cream Shop sells sundaes for $2 and banana splits for $3. On a hot summer day, the shop sold 8 more sundaes than banana splits and made $156.

2. A large pizza at Palanzio's Pizzeria costs $6.80 plus $0.90 for each topping. The cost of a large cheese pizza at Guido's Pizza is $7.30 plus $0.65 for each topping. How many toppings need to be added to a large cheese pizza from Palanzio's Pizzeria and Guido's Pizza in order for the pizzas to cost the same, not including tax?

3. The equations of two lines are 6x - y = 4 and y = 4x + 2. What is the value of x in the solution for this system of equations?

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Mathematics

12 December, 08:19

1. The Frosty Ice-Cream Shop sells sundaes for $2 and banana splits for $3. On a hot summer day, the shop sold 8 more sundaes than banana splits and made $156.

2. A large pizza at Palanzio's Pizzeria costs $6.80 plus $0.90 for each topping. The cost of a large cheese pizza at Guido's Pizza is $7.30 plus $0.65 for each topping. How many toppings need to be added to a large cheese pizza from Palanzio's Pizzeria and Guido's Pizza in order for the pizzas to cost the same, not including tax?

3. The equations of two lines are 6x - y = 4 and y = 4x + 2. What is the value of x in the solution for this system of equations?

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Answers (1)

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Claire Lawrence · Answer 1

1) Sundaes - $2; Banana Splits - $3

3x + 2 (x+8) = 156

3x + 2x + 16 = 156

5x = 156 - 16

5x = 140

x = 28 banana split; x + 8 = 28 + 8 = 36 sundaes

2) Palanzio's = 6.80 + 0.90x; Guido's = 7.30 + 0.65x

6.80 + 0.90x = 7.30 + 0.65x

0.90x - 0.65x = 7.30 - 6.80

0.25x = 0.50

x = 2 number of toppings.

6.80 + 0.90x = 7.30 + 0.65x

6.80 + 0.90 (2) = 7.30 + 0.65 (2)

6.80 + 1.80 = 7.30 + 1.30

8.60 = 8.60

3) 6x - y = 4; y = 4x + 2

6x - (4x+2) = 4

6x - 4x - 2 = 4

2x = 4 + 2

2x = 6

x = 6/2

x = 3

y = 4x + 2

y = 4 (3) + 2

y = 12 + 2

y = 14

6x - y = 4

6 (3) - 14 = 4

18 - 14 = 4

4 = 4