Find the number of medals for each country.

Question

The total number of medals won by athletes in each of the countries​ A, B,​ C, and D are four consecutive integers whose sum is 82. Find the number of medals for each country.

Answer 1

4 consecutive integers sum to 82

x + x+1 +x+2+ x+3 = 82

4x = 82- 6 = 76

x = 76/4 = 19

A=19, B=20, C=21, D=22

or did 4 consecutive integers refer to each of A through D, and not collectively to A through D?

if so

4x+3 = 19 for A

x = 4, 5, 6, 7 for A

4x+3 = 20 for B

x = 17/4 = 4.25 ... nope that doesn't work.

Answer 2

x + 2x + 3x + 4x = 82

Collect Like Terms

Division Property of an Equality; Isolates Variable to solve for x

Then, substitute in the value of x for each variable; multiply variable value of x by each co-efficient.

Result 8.2 + 16.4 + 24.6 + 32.8 = 82

Each country cannot have part of a medal, so use rounding

Country A: 8

Country B: 16

Country C: 25

Country D: 33

Answer 3

Same as my last solution yet the sum is now 85

n + n + 1 + n + 2 + n + 3 = 82

Can you solve for n and answer?