Achange jar contains nickels dimes and quarters totaling and amount of $1.90 the amount of nickels is one more than twice the number of dimes the number of quarters is one half the total number of nickels and dimes find the number of each coin in the change jar

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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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=

Also total worth of coins is $1.90

x(0.1)+(2x+1)0.05+

115x+35=380

x=3

therefore no of nickels =2*3+1=7

Quarter=5