High School

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This equation shows how the accuracy of Colin's watch is related to how long it has been since he last set it:

[tex]1.3d + 18.6 = s[/tex]

The variable [tex]d[/tex] represents the number of days that have passed since Colin last set his watch, and the variable [tex]s[/tex] represents how many seconds behind the watch is.

How many days has it been since Colin last set his watch if the watch is 97.9 seconds behind?

Answer :

The equation relating the accuracy of Colin's watch to the number of days since he last set it is given by

[tex]$$
1.3d + 18.6 = 97.9,
$$[/tex]

where [tex]$d$[/tex] is the number of days and [tex]$97.9$[/tex] is the number of seconds by which the watch is behind.

Step 1: Subtract the constant term from both sides to isolate the term with [tex]$d$[/tex]:

[tex]$$
1.3d = 97.9 - 18.6.
$$[/tex]

Calculating the right side, we have

[tex]$$
1.3d = 79.3.
$$[/tex]

Step 2: Divide both sides of the equation by [tex]$1.3$[/tex] to solve for [tex]$d$[/tex]:

[tex]$$
d = \frac{79.3}{1.3}.
$$[/tex]

Performing the division gives

[tex]$$
d = 61.
$$[/tex]

Thus, Colin set his watch [tex]$\boxed{61}$[/tex] days ago.

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