Question

latanya has $1.90 worth of nickels and dimes. she has a total of 24 nickels and dimes altogether. determine the number of nickels and the number of dimes that latanya has.
answer attempt 1 out of 2
there are nickels and dimes.

Explanation:

Step1: Define variables

Let $n$ = number of nickels, $d$ = number of dimes.

Step2: Set up total count equation

Total coins: $n + d = 24$

Step3: Set up total value equation

Value in dollars: $0.05n + 0.10d = 1.90$

Step4: Solve for one variable

From Step2: $n = 24 - d$

Step5: Substitute into value equation

$0.05(24 - d) + 0.10d = 1.90$
$1.2 - 0.05d + 0.10d = 1.90$
$1.2 + 0.05d = 1.90$

Step6: Calculate number of dimes

$0.05d = 1.90 - 1.2 = 0.70$
$d = \frac{0.70}{0.05} = 14$

Step7: Calculate number of nickels

$n = 24 - 14 = 10$

Answer:

There are 10 nickels and 14 dimes.