14. Solve the problem. A coin jar contains nickels, dimes, and quarters. There a
ID: 3411034 • Letter: 1
Question
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.
Explanation / Answer
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
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