Lesson I do not have enough savings now
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<H2>I do not have enough savings now</H2> <H3>Problem 1</H3>Andrew and Michael each wants to buy a sundae. But Andrew is 2 d ollars short, while Michael is 1 dollar short. Combined, they have exactly enough money to buy one sundae. How many dollars does one sundae cost? <B>Solution</B> <pre> Let x represents the cost of one sundae in dollars. Andrew is $2 short, so he has (x-2) dollars. Likewise, Michael has (x-1) dollars. Since together they have exactly enough to buy one sundae, x dollars, we can write: (x-2) + (x-1) = x. Solve it for x 2x - 3 = x, 2x - x = 3, x = 3. <U>ANSWER</U>. Each sundae costs 3 dollars. </pre> <H3>Problem 2</H3>Lola, Spencer and Joaquin each want to buy a sundae. But Lola is 4 dollars short, Spencer is 3 dollars short, and Joaquin is 1 dollar short. Combined, they have exactly enough money to buy one sundae. How many dollars does one sundae cost? <B>Solution</B> <pre> Let x represents the cost of one sundae in dollars. Lola is $4 short, so she must have (x-4) dollars. Likewise, Michael has (x-3) dollars and Joaquin has (x-1). Since together they have exactly enough to buy one sundae, x dollars, we can write: (x-4) + (x-3) + (x-1) = x. Solve it for x 3x - 8 = x 3x - x = 8 2x = 8 x = 8/2 = 4. <U>ANSWER</U>. Each sundae costs 4 dollars. </pre> <H3>Problem 3</H3>Mr. Lee wants to buy 5 shirts. If he buys 3 shirts, he will have $6 left. If he gets all of them, he will be $10 short. How much money does Mr. Lee have? <B>Solution</B> <pre> In accordance with the context of the problem, all the shirts have the same price. Let x be the price for one shirt. Then Mr. Lee has, from one part of the condition, 3x + 6 dollars; from the other part of the condition, he has 5x - 10 dollars. It gives you THIS EQUATION 3x + 6 = 5x - 10. Simplify and find x 6 + 10 = 5x - 3x 16 = 2x x = 16/2 = 8 dollars. One shirt costs 8 dollars. Hence, Mr Lee has 3x + 6 = 3*8 + 6 = 30 dollars. <U>ANSWER</U> </pre> <H3>Problem 4</H3>I do not have enough savings now to buy pair of shoes. If I increase my savings by 15%, I would still need another $9. If I increase my savings by 35%, I would have $17 more than I need. How much money do I have in my savings now ? <B>Solution</B> <pre> Let x = How much money you have in your savings now. Let y = the cost of the pair of shes. Then from the condition you have these two equations x + 0.15x = y - 9 dollars (1) x + 0.35x = y + 17 dollars (2) Subtract equation (1) from equation (2) to eliminate x. You will get 0.35x - 0.15x = 17 - (-9) 0.2x = 26 x = 26/0.2 = 130 dollars. <U>ANSWER</U>. Your savings now is/(are) 130 dollars. </pre> <H3>Problem 5</H3>Several people want to split a bill. If each contributes $0.35, they lack $4.40. If each contributes $0.40, they have $4.40 extra. Find the number of people. <B>Solution</B> <pre> Let X be the sum of money they need to collect. And let "n" be the number of people. According to the first scenario, 0.35*n + 4.40 = X dollars. According to the second scenario, 0.40*n - 4.40 = X dollars. It gives you an equation 0.35n + 4.40 = 0.40n - 4.40, or 4.40 + 4.40 = 0.40n - 0.35n, 8.80 = 0.05n n = {{{8.80/0.05}}} = {{{880/5}}} = 176. <U>ANSWER</U> </pre> <H3>Problem 6</H3>Bob had some money left after spending $9 on 4 files and 6 pens. If he were to buy one more file, he would be short 30 cents. If he were to buy one more pen he would have 70 cents left. What was the cost of each file ? How much money did he have at first ? <B>Solution</B> This problem is tricky. <pre> Let F be the price for each file; P be the price for each pen, and let X be the amount of money that Bob had initially. Then, based on the problem's description, we can write these THREE equations for three unknowns 4F + 6P = 900 cents (1) (he spent $9 on 4F and 6P) 5F + 6P = X + 30 cents (2) (he would be short 30 cents) 4F + 7P = X - 70 cents (3) (he would be 70 cents left) The setup is just completed. As I said at the beginning, it is tricky. But the solution of equations is simple. To solve them, first subtract equation (3) from equation ((2). You will get F - P = 100 cents. (4) Next, express F = P + 100 from (4), and substitute it into equation (1). You will get 4(P + 100) + 6P = 900 10P = 900 - 400 = 500 P = 500/10 = 50. Next, from equation (1), 4F + 6*50 = 900, 4F = 900 - 300 = 600, F = 600/4 = 150. Thus, the price for one file is $1.50; the price for one pen is P = F - 100 = 150-100 = 50 = $0.5 (from equation (4)) and X = 5F + 6P - 30 = 5*150 + 6*50 - 30 = 1020 cents = $10.20. (from equation (2) ) <U>ANSWER</U>. The price for each file is $1.50. 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