Somebody me with this math, ! 15 points for two thoughtful, well-explained, correct answers.

1. if bd = 24, cd = 8, and fe = 6, what is the measure of ge?

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[answer here]

2. if bc = 14, ef = 5, and eg = 15, what is the measure of cd?

[see same attachment]

[answer here]

In both parts, we have to apply "Proportionality Theorem" which tells, ratio of corresponding part should be equal.

1) CD/BD = FE/GE
8/24 = 6/GE

GE = 6*24 / 8
GE = 18 

2) BC/BD = EF/EG
14/BD = 5/15
BD = 42

Now, CD = BD - BC
CD = 42 - 14 = 24

Hope this helps!

1. You would set up a proportion to solve. BD/CD=GE/FE substitute the variables with numbers 24/8=GE/6 then you cross multiply and get 144=8GE divide both sides by 8 and get 18=GE.

2. First you need to find BD. BD/BC=EG/EF substitute the variables with numbers. BD/14=15/5 cross multiply 5BD=210 divide both sides by 5 and get BD=42. 42-14=24. CD=24.

Okay so n is going to represent our first number. since the second number of five times greater than n, the second number will be represented as 5n. for us to figure out the two  numbers we need to have  the value of n first. this is going to be done by adding the two numbers together, n and 5n. it can be simplified as 6n, which the problem states is equal to 72. divide 72 by 6n and you can solve for n.  n+5n=726n=72n=(72/6)n=12  now that we know the value of n, we have to multiply 5 times 12 which equals 60. so our two numbers/integers are 12 and 60