write and solve a proportion to answer the question.

34
is 60% of what number?
34w=
3
4
w
=

56.67.

Step-by-step explanation:

Let the number be x then

0.60 x = 34

x = 34/0.60

x = 56.67.

Step-by-step explanation:

Let the number be X

60% of X = 34

60/100 × X = 34

60X/100 = 34

60X = 34 × 100

60X = 3400

X = 3400/60

X = 56.6

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