Box A ( 20cm x 20cm x 20cm ) and B ( L x 20cm x 20cm ) have the same surface area (see link below). http://i.imgur.com/WOGgpM1.png What is the length of side L for this statement to be true?
There are a few ways to answer this question. You could set up an expression using what you know, or you could visually express the problem to find the solution. Imagine that you could unfold the boxes into a flat surface. You can now measure its surface area in smaller blocks. Using this method of visualizing the solution, we can find the length "L" (see link below). http://i.imgur.com/XW6yQdk.png
Rachel is trying to buy a winter jacket that she saw at Macy's the other day. She only has half of what she needs to make the purchase, but her mom said that she would lend her $20. With this $20, Rachel now has 3/5 of the total money she needs to buy the jacket. ...BUT WAIT! She found a coupon for 25% off her next purchase! Can Rachel afford the jacket? If not, how much money is she missing?
To answer this question, let’s break it down into smaller parts. A) How much does the jacket originally cost? Rachel has 1/2 of the money, and with her mom's $20, she has 3/5 of the money. From this, we can set up an expression: (1/2)X + 20 = (3/5)X , where "X" is the cost of the jacket. Step 1: Move "X" to the same side by subtracting (1/2)X from both sides of the expression 20 = (3/5)X - (1/2)X Step 2: Find a common denominator for 3/5 and 1/2 in order to subtract the fractions 20 = (6/10)X - (5/10)X --> 20 = (1/10)X Step 3: Isolate the "X" by multiplying both sides of the expression by 10 10*20 = 10*(1/10)X --> 200 = X The jacket costs $200. B) How much money does Rachel have? Rachel has 1/2 the money for the jacket that costs $200. Her mom gives her another $20. 1/2(200) + 20 --> 100 + 20 = 120 Rachel has $120. C) How much does the jacket cost with the 25% discount? If the jacket originally costs $200, with a 25% discount, it would cost: 200 - 200(0.25) or 200(0.75) The jacket would cost $150 after the 25% discount. So to answer the original question- No, Rachel does not have enough money to buy the jacket. She would need $30 more to make the purchase.
Your best friend just spoiled the season finale of Game of Thrones. Needless to say, you're angry. In your anger, you grab the closest object, the TV remote, and take your anger out on it. You squeeze and squeeze but can't seem to break it so you grab a hammer and smash it instead (don't ask where the hammer came from). Why is it easier to break things with a hammer?
First, imagine that you took your anger out on your best friend. You throw a punch or two and they throw a few back. Now imagine that instead of throwing punches, you pushed each other. Which would hurt more? Of course, the punches. Why is that? Punches hurt more because when you wind up your fist and send it flying, you increase its kinetic energy. When your flying fist makes contact with your horrible best friend, it imparts a large force on his body, causing much deserved pain. The same thing happens when you swing a hammer.