Alex and Jacob works at a toy shop that make toys. Alex takes 7 hours to make a toy, and Jacob takes 9 hours to make a toy. During a month, both of them makes 35 toys in total. If both of them have worked for almost similar number of hours how many toys have been prepared by Jacob?
Correct answer: A
Explanation
Lets say Alex has worked for x hrs., and Jacob has worked for y hrs. So, number of toys prepared by Alex is x/7, and Jacob is y/9. Since total number of toys prepared by both of them is 35.
=> x/7 + y/9 = 35.
=> 9x + 7y = (35)(63)
=> 7y = (35)(63) - 9x
=> y = (5)(63) - (9/7)x
=> y = 315 - (9/7)x
=> x is to be a multiple of 7. Also, we need to minimize the difference between x & y. Here are some possible values,
x = 126, y = 315 - (9/7)126 = 153
x = 133, y = 315 - (9/7)133 = 144
x = 140, y = 315 - (9/7)140 = 135
x = 147, y = 315 - (9/7)147 = 126
As we can see minimum difference between x and y is when x is 140 hrs. and y is 135 hrs. Thus total toys created by Jacob = y/9 = 135/9 = 15.
A
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AQuA-RAT items are crowdsourced algebra problems, not ACT questions. They carry five answer choices in the pre-2025 ACT Mathematics style and no ACT reporting category. Useful for drilling Preparing for Higher Math content; not a substitute for a real form.