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word problem - solving for y

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  • word problem - solving for y

    Hi, I'm having some difficulty grasping one step from the following question. It is a word problem but it must be answered by solving for y. Any assistance would be appreciated.

    James ran 2 miles in 12 minutes, has to run another 5 miles and wants to average 7 miles over the entire run. What will he have to run the remaining 5 miles in on average to accomplish this?

    So, total run is 7 miles. 2 miles @ 6 mins/mile + 5 miles @ "y" mins/mile (to be determined). These 2 numbers added together and divided by 7 must result in 7.

    2(6) + 5(y) = 7
    7 miles

    The answer shows

    7 x 12+5(y) =7 x 7
    7 miles

    Which results in 12 + 5(y) = 49, and then 5(y)= 49 - 12 ........ and so on.

    It is not clear to me as to why we are eliminating the 7 on one side and then multiplying the other side by 7. If the 7 is eliminated on one side by dividing by 7 miles, then what are we multiplying on the other side and why? Are we multiplying by 7 miles or 7 minutes?

    The rest of the answer that is provided from this point on makes sense to me, its just this part that I'm a bit confused about. I find that it doesn't get answered like other 'solve for y' questions.

    Thanks for your help.
    Last edited by Bryantist; 01-21-2014, 11:02 PM.

  • #2
    Usually, you would divide to eliminate something in an equation, but in this case since the equation is divided by 7 you have to get rid of this component to isolate "y". Therefore, you remove the division by multiplying on both sides.

    Thank you for clarifying this for me Police Prep