Integers and such?

1. The sum of 3 consecutive even integers is 162. Find the integers.

2. Three times the smallest of three consecutive even integers is two more than twice the largest. Find the integers.

3. The sum of three consecutive odd integers is 81. Find the integers

4. A child%26#039;s piggy bank contains 44 coins in quarters and dimes. The coins have a total value of $8.60. Find the number of quarters in the bank.

6. A coin purse contains 25 coins in nickles and dimes. The coins have a total value of $1.65. Find the number of dimes in the purse

7. A sofa costing $320 is sold for $479. Find the markup rate. Round to the nearest %.

8. A digitally recorded compact disc has a selling price of $18.90. The markup rate is 40%. Find the cost of the CD.

9. A markup rate of 25% is used on a computer that has a selling price of $2187.50. Find the cost of the computer.

10. A car stereo system that regularly sells for $425 is on sale for $318.75. Find the discount rate.

Integers and such?credit union

(1.) Let x be the middle integer. Such as:

(x - 1) + (x) + (x + 1) = 162

3x = 162

x = 54, therefore the three numbers are: 53, 54, 55

(2.) Lex 2x be an even number, thus the sequence would be

(2x - 2), (2x), (2x + 2). Now, since three times the smallest number is two more than twice the larger number, we have:

3(2x - 2) + 2 = 2(2x + 2)

(6x - 6) + 2 = 4x + 4

6x - 4 = 4x + 4

6x - 4x = 4 + 4

2x = 8

x = 4

Now, when we plug in this x into the sequence of even numbers above, we get the integers: 6, 8, 10

(3.) Let 2x +1 be an odd number. Thus we have:

[(2x + 1) - 2] + (2x +1) + [(2x + 1) +2) = 81

(2x - 1) + 2x +1 + (2x +3) = 81

2x + 2x + 2x + 3 = 81

6x = 81 - 3

6x = 78

x = 13.

Now, when we plug in x=13 into the original equation, we get the integers: 25 + 27 + 29 = 81

(4.)

(5.)

(6.) To find markup rates, simply find the difference between the original price and the final price. Then, divide this number by the original price:

479 - 320 = 159. Now,

159/320 = 0.496875

Now, multiply by 100 to make it a percent: 49.6875%

Rounding to the nearest percent: 50%

(8.) First, turn 40% into a decimal: 0.40

Now, multiply the selling price by the percent (now a decimal):

18.90 ? (0.40) = 7.56

Now, add this number to the original price:

18.90 + 7.56 = $26.46

(9.) Same thing as (8.) - I%26#039;ll leave it for you as practice.

(10.) Let x be the discount rate. First, subtract:

425 - 318.75 = 106.25

Now, solve for x:

425x = 106.25

x = 0.25

Now, multiply by 100 to get the percent: 25%