A district hospital treated 290 patients today, and each of them were either man, woman, or child. If it treated 10 more men than of children, and in equal as many men as women, how many children were treated ?  Select
A) 90  B) 80  C) 100  D) 110  E) 70
x = the number of men   y = the number of women   z = the number of children   From the first sentence we have   Equation #1: x + y + z = 290   ...A district hospital treated 70 more men than children...   Equation #2: x = 10 + z   ...in equal as many men as women...   Equation #3: x = y   Now, we can replace x with y in Equation #2   Equation #4: x - z = 10   Now, we can replace x with y in Equation #1   y + y + z = 290   Equation #5: 2y + z = 290   by adding equation #4 and equation #5 we get   x = 100   There are 100 men treated. This is 10 more than the number of children treated, so z = 90. That's the answer. Just as a check, y = 100, and   100 + 100 + 90= 
<gadget id="calculator">  100 + 100 + 90</gadget>
<output>290</output>
290.   90nswer= 90,(90)
<result>A</result>
A district hospital treated 290 patients today, and each of them were either man, woman, or child. If it treated 10 more men than of children, and in equal as many men as women, how many children were treated ?