p + d + q = 47

p = d

p + 10d + 25q = 551

Solution:

d = 16, p = 16, q = 15

Let p = number of pennies

Let d = number of dimes

Let q = number of quarters

We are then told that the number of pennies matches the number of dimes:

d = p

So we have three equations and three unknowns, so we can solve this:

47 coins total, so:

p + d + q = 47

Worth $5.51, so:

0.01p + 0.1d + 0.25q = 5.51

We know d = p. so substitute into the other two equations and simplify:

p + d + q = 47 and 0.01p + 0.1d + 0.25q = 5.51

p + p + q = 47 and 0.01p + 0.1p + 0.25q = 5.51

2p + q = 47 and 0.11p + 0.25q = 5.51

Solve the first equation for q and substitute into the other equation to solve for p:

2p + q = 47

q = 47 - 2p

0.11p + 0.25q = 5.51

0.11p + 0.25(47 - 2p) = 5.51

0.11p + 11.75 - 0.5p = 5.51

-0.39p = -6.24

p = 16

d = p, so:

d = 16

now we can solve for q:

q = 47 - 2p

q = 47 - 2(16)

q = 47 - 32

q = 15

So there were 15 quarters, 16 dimes, and 16 pennies.

Let X equal the number of pennies or dimes (they are the same).

Let Y equal the number of quarters.

2X + Y = 47 (the total number of coins)

X (pennies) + 10X (dimes) + 25Y (quarters) = 551 (total value in cents)

Use the first equation to solve for Y: Y = 47 - 2X

Plug this value into the second equation and simplify: 11X + 25Y = 551

11X + 25(47-2X) = 551

11X + 1175 - 50X = 551

-39X = -624

X = 16

Use this value of X to solve for Y: Y = 47-2X, Y = 15

So, there are 16 pennies, 16 dimes, and 15 quarters.

Always check your answer:

(16 x 1) + (16 x 10) + (15 x 25) should equal 551. And it does!

P.S. - As you can see from llaffer's answer there is more than one way to solve it but they are both correct. The beauty of math questions like these is that if you check your answer you can be 100% sure that it is correct.