For a fundraiser, Hailey raises $27, plus 1.50 for each lap she swims. What was the total amount raised by each swimmer after swimming laps. After how many laps would the two swimmers have raised the same amount of money?

For a fundraiser, Hailey raises $27, plus 1.50 for each lap she swims. Tariana raises $18, plus $3 for each lap she swims what is the total amount raised by each swimmer after swimming laps. after how many laps would the two swimmers have raised the same amount of money?

Answer:

If they swim 6 laps they would raise same amount of money.

The Total amount of money they raised is $36 after 6 laps.

Step-by-step explanation:

Let number of laps swim by the swimmers be x

Given:

Hailey raises $27, plus 1.50 for each lap she swims.

Hence It means amount raised by Hailey is the sum of $27 and 1.50 multiplied by Number of laps she swim.

Framing in equation form we get;

Amount of Money raised by Hailey = [tex]27+1.5x[/tex]

Also Given:

Tariana raises $18, plus 3 for each lap she swims.

Hence It means amount raised by Tariana is the sum of $18 and 3 multiplied by Number of laps she swim.

Framing in equation form we get;

Amount of Money raised by Tariana = [tex]18+3x[/tex]

Hence The expression representing the Total amount raised by Hailey is [tex]27+1.5x[/tex] and by Tariana is [tex]18+3x[/tex],

Now We need to find the Number of laps they swim so as the would raise the same amount of Money;

Hence equation can be framed as;

[tex]27+1.5x=18+3x\\[/tex]

Combining common terms we get;

[tex]3x-1.5x=27-18\\\\1.5x= 9\\\\x=\frac{9}{1.5} =6[/tex]

Hence If they swim 6 laps they would raise same amount of money.

Now we will find the amount they both will raise by substituting the value of x we get;

Amount of Money raised by Hailey = [tex]27+1.5x = 27+1.5\times 6 = 27+9 =\$36[/tex]

Amount of Money raised by Tariana = [tex]18+3x= 18+3\times 6 = 18+18=\$36[/tex]

Hence The Total amount of money they raised is $36 after 6 laps.