cameron, hannah and daniel are swimming laps to raise money for charity together the three swimmers swam a total of 1875 laps hannah swam twice as many laps as daniel cameron swam 125 more laps than hannah how many laps did each person swim

Question

Mathematics

Sloane Davidson

14 March, 10:54

cameron, hannah and daniel are swimming laps to raise money for charity together the three swimmers swam a total of 1875 laps hannah swam twice as many laps as daniel cameron swam 125 more laps than hannah how many laps did each person swim

+4

Answers (1)

Know the Answer?

Junior Kent · Answer 1

Hannah swam 700 laps, Cameron swan 825 laps, and Daniel swam 350 laps

Step-by-step explanation:

Step 1: 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

Step 2: 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)

2H + H/2 becomes 4H/2 + H/2 which simplifies to 5H/2

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.