A picture measuring 2 inches by 3 inches is placed inside a frame. The width between the picture and the frame is equal around the entire picture. If the area of the frame and the picture is 72 square inches, what is the width of the frame? Please explain!

  hope this helped

Step-by-step explanation:

   This is where it gets a little tricky. For example, 11x14 frames (which refers to the inside perimeter of the frame) used to frame an 8x10 image could be referred to as both an 8x10 frame or an 11x14 frame, assuming the complete frame package contains the appropriate mat board. However, an 11×14 frame with no mat will always be an 11×14 frame.

So is the frame dimension 11×14 or 8×10? The answer is neither.

If the frame size—not the mat opening—says 11×14, it is referring to the inside dimension. However, the frame will be cut slightly larger (typically 1/8 inch). This extra space allows room for the glazing, mounting board and mat board to fit without binding. It also allows for up to 1/16 inch error on the mat and glazing dimension as well as for expansion and contraction due to temperature changes.

When you’re purchasing a frame from Frame Destination, be it one of our largest or smallest like our 5x7, the size frame you select depends on whether or not you are including mat board. If you are including mat board, the frame size will be larger than the artwork size. If you are not including mat board, the frame size will match the artwork.

step-by-step explanation:

30% of $420 is 0.30($420) = $126 and $420 + $126 = $546.

or, 130% of $420 is 1.3($420) = $546.

notice that this is not the $600 original list price with which we started.

why doesn't this work?

the method does not work because 30% of $420 is not the same amount as the 30% of $600. it may seem obvious when stated this way, but it is a very common error made on problems of this type. we cannot just use the same percent and get back to the original amount because we are taking that percent of a different value.

to work problems of this type correctly, it is generally best to write an equation for the situation and then solve.

example: since (100% – 30%)(original price) = (sale price)

70% of the   (original price) is $420.

0.7x   = 420

equation image indicator

x = 600

the original cost was $600.

we may also solve this problem using the two-step method. working the problem in two steps requires us to use more algebra skills. we have to know that x = 1x (identity property of multiplicationtext annotation indicator) and that 1x – 0.3x = 0.7x (subtracting like terms). then we solve the problem as follows:

(original price) – 30%(original price) = sale price

x – 0.3x = 420

0.7x = $420

equation image indicator

x = 600

the original cost was $600.  

note that with both of the above methods we do obtain the correct original amount.

example: after a 5% pay raise, hermione is earning $22,680 per year. what was she earning before the pay raise?

105% of (original salary) = current salary

1.05x = 22,680

equation image indicator

x = 21,600

hermione earned $21,600 per year before the pay raise.

this is an example so maybe you will get how to at least do it!

a 4/6 = 9/12   not proportional

step-by-step explanation:

to find which are not proportional, we can use cross products

if it is true, they are proportional.   if it is not true, they are not proportional.

a 4/6 = 9/12

4* 12 = 6*9

48 = 54

not this is not proportional  

b 2/3 = 12/18  

2* 18 = 3 * 12

36 = 36

this is proportional

c 5/4 = 10/8  

5*8 = 4*10

40 = 40

this is proportional

d 7/5 = 35/25

7*25 = 5 * 35

175 = 175

is proportional