No. 2 alyssa has some coins in her purse consisting of pennies, nickels and dimes. She has 2 more nickels than dimes and thrice as many pennies as nickels. If the total is 0.52 dollars how many coins of each kind does she have.

number of dimes --- x

number of nickels --- x+2
number of pennies --- 3(x+2)

now considering value of these coins:

10x + 5(x+2) + 1(3)(x+2) = 52

take over

10x+5(x+2)+1(3)(x+2)=52

10x+5x+10+3(x+2)=52
10x+5x+10+3x+6=52
18x+16=52
18x=36
x=2
2 dimes
4 nickels
12 pennies

To solve this problem, we'll start by assigning variables to the unknowns in the question. Let's represent the number of dimes as 'd', the number of nickels as 'n', and the number of pennies as 'p'.

We're given two pieces of information: Alyssa has 2 more nickels than dimes and she has thrice as many pennies as nickels. This can be represented by the following equations:

1. n = d + 2 (since there are 2 more nickels than dimes)
2. p = 3n (since there are thrice as many pennies as nickels)

We also know that the total value of the coins is $0.52. To find the total value in cents, we can convert dollars to cents by multiplying by 100:

0.52 dollars = 0.52 * 100 = 52 cents

The value of the dimes in cents is 10d, the value of the nickels in cents is 5n, and the value of the pennies in cents is p.

Using this information, we can create the following equation for the total value of the coins:

10d + 5n + p = 52

Now we have a system of equations:

n = d + 2
p = 3n
10d + 5n + p = 52

Solving this system of equations will determine the values of d, n, and p.

To solve this system of equations, let's substitute the values of n and p from the second and third equations into the first equation:

n = d + 2 (equation 1)
p = 3n (equation 2)
=> p = 3(d + 2) (substituting n = d + 2 into equation 2)
=> p = 3d + 6

Now we can substitute the values of p and n from equations 2 and 3 into equation 4:

10d + 5n + p = 52 (equation 3)
=> 10d + 5(d + 2) + (3d + 6) = 52
=> 10d + 5d + 10 + 3d + 6 = 52
=> 18d + 16 = 52
=> 18d = 52 - 16
=> 18d = 36
=> d = 36 / 18
=> d = 2

Now that we have the value of d, we can substitute it back into equation 1 to find n:

n = d + 2
=> n = 2 + 2
=> n = 4

Finally, we substitute the values of d and n into equation 2 to find p:

p = 3n
=> p = 3 * 4
=> p = 12

Therefore, Alyssa has 2 dimes, 4 nickels, and 12 pennies in her purse.