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

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.

step-by-step explanation:

we are given a graph for system of inequalities.

in order to write the system of inequalities for the given graph, we need to find the inequality for each of the line separately.

let us find the slope of dotted line first.

taking two coordinates on the graph.

let us say (0,0) and (3,1).

let us find the slope of the line now.

slope of the dotted line would be =.

y-intercept of dotted line is y=0 only.

plugging slope m= and b=0 in slope-intercept form y=mx+b, we get

.

the line is shaded up of that dotted line.

therefore, for shading up we would take greater than inequality symbol > .

and because it's a dotted line we would take only > symbol in place of = sign in above equation of line.

therefore, inequality for dotted line would be

let us take two points (3,1) and (0,4) on the solid line.

slope of the solid line would be =.

for the solid line we have y-intercept b= 4.

plugging slope m= -1 and b=4 in slope-intercept form y=mx+b, we get

y = -1x + 4.

the line is shaded down of that solid line.

therefore, for shading down we would take less than inequality symbol < .

and because it's a solid line we would take ≤ symbol in place of = sign in above equation of line.

therefore, inequality for solid line would be

did u ever get the answers? i need