2. (15 points) shelly has a photo that is 7 1/3 inches tall. she wants to shrink it down to fit in a picture frame that is only 5 1/3 inches tall. the photo shop can only reduce photos by certain fractions. they can reduce it to 2/3 the original size, 3/4 the original size, or 5/9 the original size.

a. which reduction should she use so the picture fills as much of the frame as possible, without being too large?

b. how much extra space is there in the frame when she uses the reduction from part a?

c. if she had a machine that could reduce by any amount, so that she could make the reduced picture fit in the frame exactly, what fraction would the reduction be?

A. Which reduction should she use so the picture fills as much of the frame as possible, without being too large?

Find the scale factor to get rom 7 1/3 inches to 5 1/3 inches:

5 1/3  / 7 1/3 = 0.7272

Now rewrite the fraction as decimals:

2/3 = 0.667

¾ = 0.75

5/9 = 0.555

The closest scale that would still fit the frame would be 2/3 because it is under 0.727.

B. How much extra space is there in the frame when she uses the reduction from Part A?

Multiply the original size by the scale factor to use:

7 1/3 x 2/3 = 4 8/9

Now subtract the scaled size from the original size:

7 1/3 – 4 8/9 = 2 4/9 inches extra

C. If she had a machine that could reduce by any amount, so that she could make the reduced picture fit in the frame exactly, what fraction would the reduction be?

Convert the scale from part A to a fraction:  

0.72 = 72/99 which reduces to 8/11

correct answer is infinitely many solutions

step-by-step explanation:

2(2x + 3) = -4 + 2(2x + 5)

solving the above equation:

4x + 6 = -4 +4x +10

combining like terms

4x -4x = -4+10-6

0=0

since both sides are 0=0, we end up into true statement it means it has infinite many solutions.

so correct answer is infinitely many solutions