Answer:Given below
Step-by-step explanation:
We know Nickel is 5% of a dollar and dime is 10% of dollar
while quarter is 25% of dollar
Given
Let x be the no. of Dimes
therefore nickels be 2x+1
Quarter=[tex]\frac{1}{2}(2x+1+x)=\frac{1}{2}(3x+1)[/tex]
Also total worth of coins is $1.90
x(0.1)+(2x+1)0.05+[tex]\frac{1}{2}(3x+1)(0.25)=1.9[/tex]
115x+35=380
x=3
therefore no of nickels =2*3+1=7
Quarter=5
The total number of nickel, dimes, and quarters is 7, 3, and 5 respectively
Let the number of nickel be x
Let the number of dimes be y
Let the number of quarters be z
If a jar contains nickels, dimes, and quarters totaling an amount of $1.90, then:
x + y + z = 1.90
If the amount of nickels is one more than twice the number of dimes, then:
x = 1 + 2y
If the number of quarters is one half the total number of nickels and dimes
z = 1/2 (x+y)
z = 1/2(1+2y+y)
z = 1/2(3y+1)
Note that 1nickel = 0.05 of a dollar
dimes = 0.1 of a dollar
Quarters = 0.25 of a dollars
The total sum will be expressed as:
0.05(1+2y) + 0.1y + 0.25(0.5(3y+1)) = 1.9
Expand
0.05+0.1y+0.1y+.375y+0.125= 1.9
Collect like terms
0.1y+0.1y+0.375y+0.05+0.125-1.9 = 0
0.575y-1.725 = 0
0.575y = 1.725
y = 1.725/0.575
y = 3
Recall that x = 1 + 2y
x = 1 + 2(3)
x = 1 + 6
x = 7
Also z = 1/2(3y+1)
z = 1/2(3(3)+1)
z = 1/2(10)
z = 5
Hence the total number of nickel, dimes, and quarters is 7, 3, and 5 respectively
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