Math problems?

Question

1. The sum of the digits of a two digit number is 14. if the digits are received, the number is increased by 18. What is the number?

2. One number is 4 less than another number. The sum of the numbers is four times their difference. What are the two numbers?

3. How many kilograms of pure silver must be added to a 60% silver alloy to obtain 8 kilograms of a 57% silver alloy?

4. How many liters of a 35% acid solution should be mixed with a 14% acid solution to obtain 70 liters of a 20% acid solution?

5. Mr. Santos purchased 10,000 worth of stocks. One stock pays dividends at the rate of 4% per year. The other stock pays 6% per year. If Mr. Santos’ yearly income from the dividend is 500, how much of each stock does he own?

6. Cashing a check of 4000, Mrs. Cruz asked for the whole amount in 50 and 100 bills. She received a total of 53 bills. How many of each bill did she receive?

Answer 1

Only someone desperate for 10 points would take the time to do 6 of your homework problems for you. For two points, I'll set up # 1,
If "x" is one digit, the other digit is "14-x". To create a two digit number, assuming "x" is the integer in the ten's column, the number would be formed as 10*x + 14-x. Then, by reversal,
10*(14-x) + x is 18 more than the original number.

Answer 2

1. The sum of the digits of a two digit number is 14. if the digits are received, the number is increased by 18. What is the number?

Assuming received was supposed to be reversed :
x + y = 14
x = 14 - y
10x + y + 18 = x + 10y
10(14 - y) + y + 18 = (14 - y) + 10y
140 - 10y + y + 18 = 14 - y + 10y
122 - 9y = 14 + 9y
108 = 18y
6 = y
14 - 6 = 8
thus the number is 68


2. One number is 4 less than another number. The sum of the numbers is four times their difference. What are the two numbers?

x - 4 = y
x + y = 4(x - y)
x + y = 4x - 4y
x + (x - 4) = 4x - 4(x - 4)
2x - 4 = 4x - 4x + 16
2x - 4 = 16
2x = 20
x = 10
10 - 4 = y
6 = y


3. How many kilograms of pure silver must be added to a 60% silver alloy to obtain 8 kilograms of a 57% silver alloy?

Errrrmmmmm... how can you add any amount of 100% silver to 60% silver and lessen the amount of silver? The percentage would *have* to be between 100% and 60%...

4. How many liters of a 35% acid solution should be mixed with a 14% acid solution to obtain 70 liters of a 20% acid solution?

Well, I know that x + y = 70 and I seem to remember c1v1 = c2v2 but that's about all I got. Chemistry was never my strong suit. (owww, head hurts)

5. Mr. Santos purchased 10,000 worth of stocks. One stock pays dividends at the rate of 4% per year. The other stock pays 6% per year. If Mr. Santos’ yearly income from the dividend is 500, how much of each stock does he own?

x + y = 10000
x = 10000 - y
(x * .04) + (y * .06) = 500
4x + 6y = 50000
4(10000 - y) + 6y = 50000
40000 - 4y + 6y = 50000
2y = 10000
y = 5000
x = 5000
$5000 of each stock.


6. Cashing a check of 4000, Mrs. Cruz asked for the whole amount in 50 and 100 bills. She received a total of 53 bills. How many of each bill did she receive?

x + y = 53
x = 53 - y
50x + 100y = 4000
50(53 - y) + 100y = 4000
2650 - 50y + 100y = 4000
50y = 1350
y = 27
x = 26
27 $100 bills and 26 $50 bills

Answer 3

im not sure but for future homework help go to http://www.fairfaxcounty.gov/library/Homework/ and click on the link that says "Got homework? Try Live Homework Help for free one-to-one online tutoring." its actual live people on there that give you answers and help you understand better...

Answer 4

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