Answer:
Hannah swam 700 laps, Cameron swan 825 laps, and Daniel swam 350 laps
Step-by-step explanation:
<u>Step 1</u>: First we must represent this situation as a mathematical expression. We will assign variables for the three swimmers. C for Cameron, H for Hannah, and D for Daniel.
All three swam a total of 1875 laps. That is the sum of their efforts, we can write this as
C + H + D = 1875
<u>Step 2:</u> We want to use the rest of the information to create mathematical equations.
"hannah swam twice as many laps as daniel" can be written as
H = 2D (Hannah's effors is twice Daniel's effort)
"cameron swam 125 more laps than hannah" can be written as
C = H + 125 (Cameron's effort was 125 more laps than Hannah's effort)
Step 3: We can see that both equations have H in them. So we want to rewrite them both so they are in terms of H, that means solving the other variable.
H = 2D becomes H/2 = D (this is now solved in terms of D)
and
C = H + 125 is already solved in terms of C
Step 4: Substitute the new equations in to the original equation, now there will only be one variable.
C + H + D = 1875 becomes H + 125 + H + H/2 = 1875
Step 5: Now combine like terms and solve for H
2H + H/2 = 1750 (subtract 125 from both sides, combine H terms)
5H/2 = 1750 (combine 2H and H/2)
<em>2H + H/2 becomes 4H/2 + H/2 which simplifies to 5H/2</em>
Now solve the equation for H
5H = 3500 (multiply both sides by 2 to get rid of the fraction)
H = 750 (divide both sides by 5 is get H by itself)
So Hannah swan 750 laps.
Step 5: We now need to plug 750 in the both equations from step 3 to determine how many laps Cameron and Daniel swam
For Daniel
H/2 = D becomes 700/2 = D which simplifies to 350 = D
So Daniel swam 350 laps
For Cameron
C = H + 125 becomes C = 700 + 125 which simplifies to C = 825
So Cameron swam 825 laps
Step 6: Checking our work
Our equation are:
H = 700, C = 825, and D = 350
700 + 825 + 350 does equal 1875, so we have the correct values.
