Matt has more than 41 marbles and fewer than 43 marbles. Maya Has More than 47 marbles and fewer than 49 marbles

Matt has 42 marbles and Maya has 48 marbles.

Step-by-step explanation:

Matt's has more than 41, but less than 43 marbles. Since each marble has to correspond to a whole and real number, the only number between 41 and 43 is 42. Likewise the only number between 47 and 49 is 48 since Maya has more than 47 marbles but less than 49 marbles.

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4