Question

2. Juliet coaches soccer and softball. She coaches both sports for a total of 18 hours each day. The soccer practice lasts 1.5 hours more than twice times as long as the softball practice.
(a) Write a system of equations to model the situation. Be sure to define your variables.
(b) How many hours each day does Juliet spend coaching each sport?
Show your work. Be sure to label appropriately.

Answer 1

An equation is formed of two equal expressions. Juliet teaches softball for 5.5 hours, while she teaches football for 12.5 hours.

What is an equation?

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

A.) Let the amount of time spent on soccer be represented by y, while the amount of time spent on softball is represented by x. Therefore, we can write,

x+y=18

y=2x+1.5

Hence, the system of equations to model the situation is x+y=18 and y=2x+1.5.

B.) Substitute the value of y from the second equation in the first equation, therefore,

x+y=18

x+2x+1.5=18

3x = 16.5

x = 5.5 hours

Substitute the value of x in the second equation, we will get,

y=2x+1.5

y=2(5.5)+1.5

y=11+1.5

y=12.5 hours

Hence, Juliet teaches softball for 5.5 hours, while she teaches football for 12.5 hours.

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