Daily Practice

Solution

Let's say that the first strand of pasta he had is x. The first time he takes a bite of this strand will make it 2 pieces. This is x - 3. The second time he takes the bites of EACH strand will become (x - 3) * 3(2). The 2 is for the two bites he took, 1 for each strand. This equation is showing that for every bite that he is taking, he is taking off 3 inches. This is being showed in the 3(2). He took 2 bites, each taking off 3 inches. Now, the problem is stating that their are 10 pieces of pasta and the TOTAL length is 17 inches. We have to plug in the total number of bites to the equation (x - 3) * 3( ). To find this out, we can see that for the number of strands there are, he took 1 less bite than that number. For example, if there are 2 pieces, he took 1 bite to get those. Since there are 10 pieces, he took 9 bites. The equation then becomes, (x - 3) * 3(9) = 17. To solve this, x = 44. Therefore, the answer is boxed{textbf{(D) } 44}. ~~Brainiacs77~~

Solution

Margie can afford $20/4=5$ gallons of gas. She can go $32cdot5=boxed\{textbf\{(C)\}~160\}$ miles on this amount of gas. ==Video Solution (CREATIVE THINKING)== https://youtu.be/YNNTewVLbyU ~Education, the Study of Everything ==Video Solution== https://youtu.be/mav136CA3eQ ~savannahsolver

Solution

Let the original price of an item be $x$. First, everything is half-off, so the price is now $frac\{x\}\{2\}\; =\; 0.5x$. Next, the extra coupon applies 20% off on the sale price, so the price after this discount will be $100\%\; -\; 20\%\; =\; 80\%$ of what it was before. (Notice how this is not applied to the original price; if it were, the solution would be applying 50% + 20 % = 70% off the original price.) $80\%\; cdot\; 0.5\; x\; =\; frac\{4\}\{5\}\; cdot\; 0.5\; x\; =\; 0.4x$ The price of the item after all discounts have been applied is $0.4x\; =\; 40\%\; cdot\; x$. However, we need to find the percentage off the original price, not the current percentage of the original price. We then subtract $40\%\; x$ from $100\%\; x$ (the original price of the item), to find the answer, $boxed\{textbf\{(D)\}\; 60\}$.

Solution

The inner unshaded region is a 4×4 grid = 16 squares. The boundary squares are the outer ring of the 6×6 grid.

Solution

We group the addends inside the parentheses two at a time: begin{align*} -1 + 2 - 3 + 4 - 5 + 6 - 7 + ldots + 1000 &= (-1 + 2) + (-3 + 4) + (-5 + 6) + ldots + (-999 + 1000) \ &= underbrace{1+1+1+ldots + 1}_{text{500 1's}} \ &= 500. end{align*} Then the desired answer is $4\; times\; 500\; =\; boxed\{textbf\{(E)\}\; 2000\}$. ==Video Solution== https://youtu.be/4Gy1CrYTDHA ~savannahsolver ==Video Solution by OmegaLearn== https://youtu.be/TkZvMa30Juo?t=3074 ~ pi_is_3.14