Mrs. long has a total of 43 children in her class. the number of girls is one more than twice the number of boys. how many boys and girls does she have in her class?

14 boys and 29 girls. The way I figured it out is I tried thinking of a number that  could be multiplied by 2 and added to the original number and I got 14, and doing the math, 14 times 2 is 28, and 28 plus 14 is 42, and 42 plus 1 is 43.

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

step-by-step explanation:

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