Daily Practice

Solution

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Solution

We should notice that we can turn the information we are given into a linear equation and just solve for our set variables. I'll use the variables x and y for the scores on the last two tests. frac{76+94+87+x+y}{5} = 81, frac{257+x+y}{5} = 81. We can now cross multiply to get rid of the denominator. 257+x+y = 405, x+y = 148. Now that we have this equation, we will assign y as the lowest score of the two other tests, and so: x = 100, y=48. Now we know that the lowest score on the two other tests is boxed{textbf{(A)} 48}. ~ aopsav

Solution

Let m and n be positive integers such that m>n and m+n=28. It follows that m=2n+d for some positive integer d. We wish to find the number of possible values for d. By substitution, we have (2n+d)+n=28, from which d=28-3n. Note that n=1,2,3,ldots,9 each generate a positive integer for d, so there are boxed{textbf{(D) } 9} possible values for d. ~MRENTHUSIASM ==Video Solution by Math-X (First understand the problem!!!!)== https://youtu.be/oUEa7AjMF2A?si=q1GMT9DB8-AY0Ld5&t=1882 ~Math-X ==Video Solution (A Clever Explanation You’ll Get Instantly)== https://youtu.be/tYWp6fcUAik?si=V8hv_zOn_zYOi9E5&t=1640 ~hsnacademy ==Video Solution (CREATIVE THINKING!!!)== https://youtu.be/YnRJ1Q0GxgU ~Education, the Study of Everything ==Video Solution== https://youtu.be/Ij9pAy6tQSg?t=1110 ~Interstigation ==Video Solution== https://youtu.be/p29Fe2dLGs8?t=139 ~STEMbreezy ==Video Solution== https://youtu.be/P3IgH0ns-7M ~savannahsolver ==Video Solution== https://youtu.be/yT-9qbMw8y8 ~harungurcan ==Video Solution by Dr. David== https://youtu.be/j-CqnzH_wDg

Solution

After Gilda gives $20$% of the marbles to Pedro, she has $80$% of the marbles left. If she then gives $10$% of what's left to Ebony, she has $(0.8*0.9)$ = $72$% of what she had at the beginning. Finally, she gives $25$% of what's left to her brother, so she has $(0.75*0.72)$ $boxed\{textbf\{(E)\}\; 54\}$ of what she had in the beginning left.

Solution

The only option that is easily divisible by 55 is 110, which gives 2 hours of travel. And, the formula is frac{15}{30} + frac{110}{55} = frac{5}{2}. And, text{Average Speed} = frac{text{Total Distance}}{text{Total Time}}. Thus, frac{125}{50} = frac{5}{2}. Both are equal and thus our answer is boxed{textbf{(D)} 110}.