7) katie is baking muffins for a picnic. she can bake 24 muffins in 45 minutes. at this rate, how
many muffins can she bake in 90 minutes and how do you know?

Katie can bake 48 muffins in 90 minutes.

Step-by-step explanation:

So, as you can see, it says she can bake 24 muffins in 45 mins. Some you make that a fraction:

24/45. The question asks how many muffins she can bake in 90 mins. So, next to the first fraction (proportion) write x/90.

Why x? Because you don't know how many muffins she made, so you'll use that to replace the number for now. X is the numerator because on the last proportion, you put the number of minutes as the denominator. X= how many muffins Katie baked.

So, you cross multiply. Multiply one numerator by the others denominator. Like this: 24×90 and 45×X. Write the answers under the denominator (Ex: 24 X

45 90

45x = 2160

Now, separate the variable (x) and the constant (45). To do something you must divide. Divide it by 45 to get x. Then, place your equal sign on the right side of that. Now, whatever you do to one side of the equal sign you must do to the other. So, divide 2160 by 45. If done coorectly, you should've gotten 48. X=48 muffins. Therefore, Katie baked 48 muffins.

Sorry about the length! I kinda got carried away lol

Also, for the explanation for how you know, my work above should explain that.

Well, I hope I was helpful!

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