**Problem 1 :**

Solve :

0.7n + 0.33 = 0.3n + 0.5

**Problem 2 :**

David walks from his house to the zoo at a constant rate. After walking 0.75 mile, he meets his brother Daniel, and they continue walking at the same constant rate. When they arrive at the zoo, David has walked for 0.5 hour and Daniel has walked for 0.2 hour. What is the rate in miles per hour at which the brothers walked to the zoo ?

**Problem 1 :**

Solve :

0.7n + 0.33 = 0.3n + 0.5

**Solution :**

**Step 1 : **

In the second term 0.33 on the left side, we have two digits (more number of digits) after the decimal.

So, multiply both sides of the equation by 10² ( = 100).

100(0.7n + 0.33) = 100(0.3n + 0.5)

100(0.7n) + 100(0.33) = 100(0.3n) + 100(0.5)

70n + 33 = 30n + 50

**Step 2 : **

Subtract 30n from both sides.

40n + 33 = 50

Subtract 33 from each side.

40n = 17

Divide each side by 40.

40n/40 = 17/40

n = 0.425

**Problem 2 :**

David walks from his house to the zoo at a constant rate. After walking 0.75 mile, he meets his brother Daniel, and they continue walking at the same constant rate. When they arrive at the zoo, David has walked for 0.5 hour and Daniel has walked for 0.2 hour. What is the rate in miles per hour at which the brothers walked to the zoo ?

**Solution :**

**Step 1 : **

Write an expression for the distance from the brothers’ house to the zoo, using the fact that distance equals rate times time.

Let r be the walking rate of both David and his brother Daniel.

Distance from the brothers’ house to the zoo

= 0.2r

**Step 2 : **

Write an expression for the distance from the David's house to the zoo, using the distance from his brother's house to the zoo.

Distance from Davids’ house to the zoo

= 0.75 + 0.2r -----(1)

**Step 3 :**

Write an expression for the distance from the David's house to the zoo, using David's total walking time 0.5 hour.

Distance from Davids’ house to the zoo

= 0.5r -----(1)

**Step 4 : **

Both (1) and (2) represent the distance from David's house to the zoo.

So, we have

(1) = (2)

0.75 + 0.2r = 0.5r

**Step 5 :**

In the first term 0.75 on the left side, we have two digits (more number of digits) after the decimal.

So, multiply both sides of the equation by 100.

100(0.75 + 0.2r) = 100(0.5r)

100(0.75) + 100(0.2r) = 50r

75 + 20r = 50r

**Step 6 :**

Subtract 20r from both sides.

75 = 30r

Divide both sides by 30.

2.5 = r

So, the brothers’ constant rate of speed was 2.5 miles per hour.

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