If mike Kevin and Dustin all collect baseball cards and Dustin and Kevin has 81 altogether and Dustin and Mike have 96 altogether and Kevin and mike have 93 together how many do each of the boys have?

Dustin has 42 cards.

Mike has 54 cards.

Kevin has 39 cards

Step-by-step explanation:

subtract (Dustin + Mike) – (Dustin + Kevin) or 96 – 81.

Think of it like

Dustin + Mike – Dustin – Kevin

Dustin – Dustin + Mike – Kevin

Mike – Kevin

Since 96 – 81 = 15, Mike – Kevin = 15

Add (Kevin + Mike) + (Mike – Kevin) or 93 + 15.

Think of it like...

Kevin + Mike + Mike – Kevin

Kevin – Kevin + Mike + Mike

Mike + Mike

Since 93 + 15 = 108, Mike + Mike = 108. If you divide, Mike had 54 cards. That means that you can find Kevin’s cards by using 93 – 54 or 39. You can then find Dustin’s cards by using 81 – 39 = 42.

Check:

Dustin’s cards + Kevin’s cards = 42 + 39 = 81

Dustin’s cards + Mike’s cards = 42 + 54 = 96

Mike’s cards + Kevin’s cards = 54 + 39 = 93

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

answer: b.36 feet

step-by-step explanation: