Question

in the 2014 winter olympics in sochi russia earned 4 more gold medals than bronze. The number of silver medals earned was 7 less than twice the number of bronze medals. Russia earned a total of 33 medals. How many of each kind did Russia earn?

Answer 1

Answer: Russia earned 13 gold medals, 11 silver medals and 9 bronze medals.

Step-by-step explanation:

Let x represent the number of gold medals that Russia earned.

Let y represent the number of silver medals that Russia earned.

Let z represent the number of bronze medals that Russia earned.

Russia earned a total of 33 medals. This means that

x + y + z = 33 - - - - - - - - - - - 1!

In the 2014 winter olympics in sochi russia earned 4 more gold medals than bronze. This means that

x = z + 4

The number of silver medals earned was 7 less than twice the number of bronze. This means that

y = 2z - 7

Substituting x = z + 4 and y = 2z - 7 into equation 1, it becomes

z + 4 + 2z - 7 + z = 33

4z - 3 = 33

4z = 33 + 3 = 36

z = 36/4 = 9

x = z + 4 = 9 + 4

x = 13

y = 2z - 7 = 2 × 9 - 7

y = 11