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janesa has 24 coins in her pocket worth exactly $1.00. she tells her younger brother jackson that he can have the coins if he correctly guesses how many of each coin she has. she gives him the hint that there are only nickels and pennies. complete the equation that represents the total value of the nickels and p pennies 5( blank ) + p = 100

Respuesta :

Answer:

Number of Nickels = 19

Number of pennies = 5

Step-by-step explanation:

The type of coins that Janessa has = nickels and pennies.

Janessa has a total number of 24 coins

The sum of the nickels and pennies = $1.00

Let us represent the number of nickels as x

The number of pennies as y

Hence, our system of equations is :

x + y = 24..... Equation 1

x = 24 - y

A nickel is worth 5 cents.

1 nickel = $0.05

A penny is worth 1 cent.

1 penny = $0.01

Therefore,

$0.05× x + $0.01 × y= $1.00

0.05x + 0.01y = 1.00........Equation 2

Substitute 24 - y for x in Equation 1

0.05(24 - y) + 0.01y = 1

1.2 - 0.05y + 0.01y = 1

1.2 - 1 = 0.05y - 0.01y

0.2 = 0.04y

y = 0.2/0.04

y = 5

We have 5 pennies

x = 24 - y

x = 24 - 5

x = 19

We have 19 nickels

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