Marie and Jorge are both trying to lose weight. After 3 months they compared their weight loss. Marie’s weight went from 175 to 150. Jorge’s weight went from 190 to 180. Which statements are true regarding their weight loss? Select three options. Jorge’s weight change was approximately 5%.
Marie’s weight change was approximately 14%.
Marie had the greater percent change.
Jorge had the greater percent change.
Marie’s weight change was approximately 1.4%.

Jorge's weight percent decrease is (190-180)÷190, or amount of change/original amount. Simplified, 10÷190=5.2637157894...%, approximately equal to 5%. The first option is correct. Marie's percent decrease is (175-150)÷175. Simplified, that is 25÷175=14.2857142857...%, which is about 14%. The second option is correct. Clearly, we can tell that Marie had the greater percent change, about 14% to about 5%. Also clearly, Jorge did not have the greater percent change, so we can tell Option 4 is wrong. We already know that Jorge's change is about 5% and Marie's is about 14%, so they can't be about 0.5% or about 1.4%. Options 5 and 6 are incorrect. The correct answers are 1, 2, and 3.

where are the choices?

geometry: triangles

solvers

lessons

answers archive

call the larger triangle abc

then the smaller triangle cde is similar to abc (all angles are equal, aaa).  

ab is the side that is 36, and we wish to find de, the side corresponding to ab

area_cde = area_abc - area_cde --> area_abc / area_cde = 2

let x=length of de

ratio of areas = (ratio of sides)^2

+2+=+%2836%2fx%29%5e2+

+2+=+1296%2fx%5e2+

++x%5e2+=+1296%2f2+=+648+

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