Question

select the correct answer.
a total of 22 dimes and nickels have a value of $1.90. if d represents the number of dimes and n represents the number of nickels, which system of equations models this situation?

a. ( d + n = 1.9 )
( 0.1d + 0.05n = 22 )

b. ( d + n = 22 )
( 0.1d + 0.05n = 1.9 )

c. ( d + n = 1.9 )
( 0.1d + 0.5n = 22 )

d. ( d + n = 22 )
( 0.1d + 0.5n = 1.9 )

Explanation:

Step1: Analyze the number of coins

The total number of dimes (\(d\)) and nickels (\(n\)) is 22, so the first equation should be \(d + n = 22\).

Step2: Analyze the value of coins

A dime is worth \$0.10 and a nickel is worth \$0.05. The total value of the coins is \$1.90. So the second equation is \(0.1d + 0.05n = 1.9\).

Answer:

B. \( d + n = 22 \)
\( 0.1d + 0.05n = 1.9 \)