Question 1187750
let a equal the the number of hours spent on plan A.
let b equal the number of hours spent on plan B.


on friday, there were 3 who did plan A and 2 who did plan B for a total of 7 hours.


on saturday, there were 8 who did plan A and 4 who did plan B for a total of 17 hours.


you have two equations that need to be solved simultaneously.
that means the same value of a and b for both equations.


the requations are:


3a + 2b = 7
8a + 4b = 17


multiply both sides of the first equAtion by 2 and leave the second equation as is to get:


6a + 4b = 14
8a + 4b = 17


subtract the first equation from the second to get:


2a = 3


solve for a to get:


a = 3/2


replace a with 3/2 in either equation to get:


6a + 4b = 14 becomes 6 * 3/2 + 4b = 14 which becomes 9 + 4b = 14
8a + 4b = 17 becomes 8 * 3/2 + 4b = 17 which becomes 12 + 4b = 17


solve for b in both equations to get:


4b = 14 - 9 which becomes 4b = 5 which becomes b = 5/4.
4b = 17 - 12 which becomes 4b = 5 which becomes b = 5/4.


you have:


a = 3/2 and b = 5/4.


replace a and b in your original equaiton to see if they are true.


3a + 2b = 7 becomes 3 * 3/2 + 2 * 5/4 = 7 which becomes 9/2 + 10/4 = 7 which becomes 18/4 + 10/4 = 7 which becomes 28/4 = 7 which becomes 7 = 7, confirming the values of a and b are good for the first equation.



8a + 4b = 17 becomes 8 * 3/2 + 4 * 5/4 = 17 which becomes 24/2 + 20/4 = 17 which becomes 48/4 + 20/4 = 17 which becomes 68/4 = 17 which becomes 17 = 17, confirming the value of a and b are good for the second equation.


your solution is that plan A workout lasts 1.5 hours and plan B workout lasts 1.25 hours.


let me know if you have any questions.


theo