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Fang wants to ride his bicycle 45.6 mi this week. He has already ridden 20 mi. If he rides for four more days, write and solve an equation which can be used to determine in the average number of miles he would have to ride each day to meet his goal

5 answers

To help Fang determine the average number of miles he needs to ride each day for the next four days, we can set up the problem as follows:

  1. Total Mileage Goal: Fang wants to ride a total of 45.6 miles.

  2. Miles Ridden So Far: Fang has already ridden 20 miles.

  3. Miles Remaining: To find out how many miles Fang has left to ride, we subtract the miles he has already ridden from his total goal:

    \[ \text{Miles Remaining} = 45.6 , \text{mi} - 20 , \text{mi} = 25.6 , \text{mi} \]

  4. Days Left to Ride: Fang plans to ride for 4 more days.

  5. Average Miles per Day: Let \( x \) be the average number of miles Fang needs to ride each day for the next four days. The equation can be set up like this:

    \[ 4x = 25.6 \]

    Here, \( 4x \) represents the total miles Fang would ride over the 4 days, and we want that total to equal the miles remaining (25.6 miles).

  6. Solving for \( x \):

    To find \( x \), divide both sides of the equation by 4:

    \[ x = \frac{25.6}{4} \]

    \[ x = 6.4 \]

Thus, Fang needs to ride an average of 6.4 miles each day for the next four days to meet his goal of 45.6 miles for the week.

K but make a single line equation

Sure! Here’s the single line equation that represents the total miles Fang needs to ride over the next four days:

\[ 4x = 45.6 - 20 \]

Where \( x \) is the average number of miles Fang needs to ride each day.

To solve for \( x \):

\[ x = \frac{45.6 - 20}{4} \]

This simplifies to:

\[ x = \frac{25.6}{4} = 6.4 \]

So, the equation is \( 4x = 25.6 \).

K but can you write the equation in the form of AM + b = c

Sure! We can rewrite the equation in the form of \( AM + b = c \).

Let's define:

  • \( M \) as the average miles Fang needs to ride each day (which we want to find),
  • \( A \) as the number of days left to ride (which is 4),
  • \( b \) as the miles already ridden (which is 20),
  • \( c \) as the total mileage goal (which is 45.6).

We can rearrange it as follows:

Given our earlier equation:

\[ AM + b = c \]

Substituting \( A = 4 \), \( M = x \), \( b = 20 \), and \( c = 45.6 \):

\[ 4M + 20 = 45.6 \]

This is now in the desired form \( AM + b = c \).