Grades 9-10 Video Solutions 2014-Levels 9&10 Video Solutions 2014 problem15

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Question number 15. A new kind of crocodile has been discovered in Africa. The length of its tail is a third of the crocodile's entire length. Its head is 93  centimeters long and the length of the head is a quarter of the crocodile's length without the tail. How long is the crocodile in centimeters? Let's write  down equations describing the information we are given. I will call H the head of the crocodile and we know that is equal to 93 centimeters. I will  call T the tail and I will call C the crocodile's length.  Okay, so from the information that's given we know that the length of the tail, so T, is equal to one-third, so one-third times the crocodile's entire  length, so one-third times C. That's from sentence two. From sentence three we know that the head is 93 centimeters, H is equal to 93 centimeters, and also that is  at the same time equal to a quarter, so one-fourth, times the length of the crocodile minus its tail, so C minus T. And that's all the information that  we're given, so now we can solve for C. Our job is to find the crocodile's total length, C. So from equation two we see that 93 centimeters multiplied by four  is equal to four times one-fourth times C minus T, and that is equal to simply C minus T. From the first equation we know that T is equal to one-third C. We have  then that four times 93 centimeters is C minus one-third C, which is two-thirds C. So three-halves times four times 93 centimeters is equal to C, and this we  got by multiplying the above equation by three-halves on both sides, and multiplying again four times three-halves is six times 93 centimeters is what we  are looking for, that is 600 minus 7 times 6, and the end result is then 558. 558 centimeters, so that is answer A here, the crocodile is 5 meters 58  centimeters long or 558 centimeters in length.

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