At your favorite restaurant 6 pizzas and 2 salads cost $80, and 3 pizzas and 4 salads cost $61. Write a system of equations and solve to find the individual price of pizzas and salads.

Question

Need help Asap, this question is hard please answer it as I need help with this and it's due very soon.

Answer 1

let x = pizza and y = salad

We can write 2 equations from the information given:

6x + 2y = 80 and

3x + 4y = 61

If we multiply the first equation by 2 so we have the same number of y in each equation we get:

2(6x + 2y = 80) or 12x +4y = 160

Then we can subtract the second equation from the first equation (which has been multiplied by 2);

12x +4y = 160

-(3x + 4y = 61)____

9x = 99

Now solving for x we get:

9x = 99_ or x = 11

9 9

We can plug our newly found x back into either equation and solve for y (I'll use the first equation):

6(11) + 2y = 80

66 + 2y = 80

2y = 14

y = 7

Therefore, pizzas cost $11 and salads cost $7.

Answer 2

You need to FOLLOW the steps !!!

6p + 2s = 80

3p + 4s = 61

Eq1 - 2 * Eq2:

(6p + 2s) - 2(3p+4s) = 80 - 2*61

6p+2s - 6p - 8s = 80 - 122

-6s = -42

s = 7

Per Eq2:

3p + 4(7) = 61

3p + 28 = 61

3p = 33

p = 11

the pizza pie costs $11

and the salad costs $7

Answer 3

Let P = pizzas and S = Salads

So,

1. six pizza and two salads cost $80 becomes:
2. 6P + 2S = 80,
3. we can simplify this equation by dividing everything by 2 to get:
4. 3P +S = 40, and so we can solve for S by subtracting 3P from both sides:
5. S = 40 - 3P
6. three pizzas and four salads cost $61 becomes:
7. 3P + 4S = 61
8. Substitute in S = 40 - 3P to this equation to get:
9. 3P +4(40 - 3P) = 61
10. Distributing the 4 gives us:
11. 3P + 160 - 12P = 61
12. Collecting like terms:
13. -9P +160 = 61
14. Subtract 160 from both sides:
15. -9P = -99

At this point, you can finish this problem by solving for P and then using that value of P to figure out the cost of a salad...recall S = 40-3P

Good luck.

Let me know if this helped you solve the problem or if you need some more clarification