14 Solve the problem A coin jar contains nickels dimes and q

14.

Solve the problem.

A coin jar contains nickels, dimes, and quarters. There are 47 coins in all.

There are 12 more nickels than quarters.

The value of the dimes is $3.70 less than the value of the quarters.

How many coins of each type are in the jar?

12. Solve the problem.

Stan invested $11,000, part at 3% and part at 12%. If the total interest at the end of the year is $1140, how much did he invest at 3%?

6. Solve the problem.

Ryan divides $17,000 into three accounts paying 2%, 4%, and 6%. The annual interest from the three accounts is $800. If Ryan has $2000 more invested at 4% than at 2%, how much does Ryan have invested at 6%?

5. The length of a rectangle is 5 in. more than twice its width. If the perimeter of the rectangle is 28 in .find the width of the rectangle.

Solution

14)

Let the number of nickel be \"x\"

let the number of dimes be \"y\"

let the number of quarters be \"z\"

total number of coins = 47

x + y + z = 47              (1)

There are 12 more nickels than quarters.

x = z + 12                  (2)

Value of 1 nickle = 0.05 $

Value of 1 dimes = 0.10 $

Value of 1 Quarter = 0.25$

The value of the dimes is $3.70 less than the value of the quarters

0.10 * y + 3.70 = 0.25 * z                 // multiplying both sides by 100

10y + 370 = 25 z              (3)

from (1) and (2)

x + y + z = 47                     // x = z +12 (2)

z + 12 + y + z = 47

y + 2z = 35           

y = 35 - 2z               (4)

from (3) and (4)

10 (35 - 2z) + 370 = 25z

350 - 20z + 370 = 25 z

720 = 45z

z = 16

from (4)

y = 35 -2z

y = 35 - 32

y = 3

from (2)

x = z + 12

x = 16 + 12

x = 28

x = 28 , y = 3 and z = 16

12)

let the amount invested in 3% be \"x\"

therefore, the amount invested in 12 % be \"11000 - x\"

interest earned = $ 1140

interest earned = principal * fractional rate * time

interest earned for 3 % = x * 0.03 * 1 = 0.03x            (1)

interest earned for 12 % = (11000-x)*0.12*1 = 1320 - 0.12x (2)

frrom (1) and (2)

0.03 x + 1320 - 0.12 x = 1140

-0.09x = -180

x = 2000

therefore money invested in 3 % = $ 2000

money invested in 12% = 11000 - 2000 = $ 9000

.

5)

let the length of reactangle be \"l\"

let the width be \"w\"

The length of a rectangle is 5 in. more than twice its width

l = 2w + 5      (1)

perimeter of the rectangle = 28

2(w+l) = 28

w + l = 14     (2)

w + 2w + 5 = 14      // from (1) l = 2w+ 5

3w = 9

w = 3 in

from (1)

l = 2w + 5

l = 2*3 + 5

l = 6 +5

l = 11 in

width = 3 inch