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27 September, 10:06

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

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  1. 27 September, 10:19
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    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.
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