Grace has $105 to buy a cake and pizza for her cousin’s birthday party. She knows she needs to set aside $25 for the cake, and the rest of the money she can spend on pizzas. Each pizza costs $9.25. How many pizzas can Grace afford to buy? a. write and solve an inequality to answer the question

b. each pizza serves 4 people. if 22 people reply that they will attend the party, how many pizzas should grace buy? explain your reasoning.

im sorry its alot but this will help me lots

A. She can buy 8 pizzas; B. At least 6 pizzas.

Step-by-step explanation:

Since Grace has $105, we can set our inequality to be less than or equal to that amount of money.  We also know she needs to spend $25 on the cake no matter what.  Assuming x is the amount of pizzas she can buy and each pizza costs $9.25, our inequality looks like this:

9.25x + 25 ≤ 105

To solve this inequality, we first subtract 25 from both sides, which gives us:

9.25x ≤ 80

Then we divide by 9.25 on both sides, giving us:

x ≤ 8.6486

Since Grace is only able to buy whole pizzas, the most she can buy is 8 pizzas.

If each pizza serves 4 people and there are 22 people attending, we need to be able to feed 22 or more people.  We can use this inequality, where x is still the number of pizzas.

4x ≥ 22

Dividing both sides by 4, we get:

x ≥ 5.5

Again, assuming we can only buy whole pizzas, we would need at least 6 pizzas to feed the entire party.

37/3

step-by-step explanation:

step 1: simplify both sides of the equation.

7x+8(x+

1

4

)=3(6x−9)−8

7x+(8)(x)+(8)(

1

4

)=(3)(6x)+(3)(−9)+−8(distribute)

7x+8x+2=18x+−27+−8

(7x+8x)+(2)=(18x)+(−27+−8)(combine like terms)

15x+2=18x+−35

15x+2=18x−35

tep 2: subtract 18x from both sides.

15x+2−18x=18x−35−18x

−3x+2=−35

step 3: subtract 2 from both sides.

−3x+2−2=−35−2

−3x=−37

step 4: divide both sides by -3.

−3x

−3

=

−37

−3

x=

37

3

$4034.40

the perimeter of the field is the sum of the lengths of the four sides:

47 yd + 158 yd + 47 yd + 158 yd = 410 yd

the cost of 3 ft (1 yd) of fence is 3×$3.28 = $9.84.

so the cost of jake's wood perimeter fance is

(410 yd) × ($9.84 /yd) = $4034.40