we will assume that coins are: pennies, nickles, dimes and quarters

let

p = the number of pennies

n = the number of nickles

d = the number of dimes

q = the number of quarters

there are total of 10 coins means:

p + n + d + q = 10

and the total value is 87 cents or:

p + 5n + 10d + 25q = 87

5n + 10d + 25q = 87 - p

since the left side is divisible by 5 for the right side we will take p = 2 to get a number divisible by 5

5n + 10d + 25q = 87 - 2

5n + 10d + 25q = 85 divide both sides by 5

n + 2d + 5q = 17

n = 17 - 2d - 5q

and also plug this value into 2 + n + d + q = 10

2 + 17 - 2d - 5q + d + q = 10

19 - d - 4q = 10

d + 4q = 9

q = 2

d = 1

n = 17 - 2*1 - 5*2

n = 5

thus we have:

2 pennies, 5 nickles, 1 dime and 2 quarters

indeed:

2*1 + 5*5 + 1*10 + 2*25 = 2 + 25 + 10 + 50 = 87.