8.7 Applications  (Page 3/4)

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When the same number is added to both the numerator and denominator of the fraction $\frac{3}{7},$ the result is $\frac{2}{3}.$ What is the number?

When the same number is added to both the numerator and denominator of the fraction $\frac{5}{8},$ the result is $\frac{3}{4}.$ What is the number?

When the same number is added to both the numerator and denominator of the fraction $\frac{3}{8},$ the result is $\frac{1}{6}.$ What is the number?

When the same number is added to both the numerator and denominator of the fraction $\frac{7}{9},$ the result is $\frac{2}{3}.$ What is the number?

When the same number is subtracted from both the numerator and denominator of $\frac{1}{10},$ the result is $\frac{2}{3}.$ What is the number?

When the same number is subtracted from both the numerator and denominator of $\frac{3}{4},$ the result is $\frac{5}{6}.$ What is the number?

One third of a number added to the reciprocal of number yields $\frac{13}{6}.$ What is the number?

Four fifths of a number added to the reciprocal of number yields $\frac{81}{10}.$ What is the number?

One half of a number added to twice the reciprocal of the number yields 2. What is the number?

One fourth of a number added to four times the reciprocal of the number yields $\frac{-10}{3}.$ What is the number?

One inlet pipe can fill a tank in 8 hours. Another inlet pipe can fill the tank in 5 hours. How long does it take both pipes working together to fill the tank?

One pipe can drain a pool in 12 hours. Another pipe can drain the pool in 15 hours. How long does it take both pipes working together to drain the pool?

A faucet can fill a bathroom sink in 1 minute. The drain can empty the sink in 2 minutes. If both the faucet and drain are open, how long will it take to fill the sink?

A faucet can fill a bathtub in $6\frac{1}{2}$ minutes. The drain can empty the tub in $8\frac{1}{3}$ minutes. If both the faucet and drain are open, how long will it take to fill the bathtub?

An inlet pipe can fill a tank in 5 hours. An outlet pipe can empty the tank in 4 hours. If both pipes are open, can the tank be filled? Explain.