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nlexa [21]
3 years ago
12

Country ​A, Country​ B, and Country C won a total of 130 medals. Country B won 10 more medals than Country C. Country A won 38 m

ore medals than the total amount won by the other two. How many medals did each of the top three countries​ win?
Mathematics
1 answer:
snow_lady [41]3 years ago
8 0

Answer:

Country ​A = 84

Country​ B = 28

Country C = 18

Step-by-step explanation:

Country ​A, Country​ B, and Country C won a total of 130 medals;

A + B + C = 130 ......1

Country B won 10 more medals than Country C;

B = C + 10 .......2

Country A won 38 more medals than the total amount won by the other two;

A = B + C + 38 ........3

Substituting equation 3 to 1;

(B+C+38) + B+C = 130

2B + 2C + 38 = 130 .......4

Substituting equation 2 into 4;

2(C+10) + 2C + 38 = 130

4C + 58 = 130

4C = 130-58 = 72

C = 72/4 = 18

B = C + 10 = 18 + 10 = 28

A = B + C + 38 = 18 + 28 + 38 = 84

Country ​A = 84

Country​ B = 28

Country C = 18

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Explanation:

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One fifth of a number is the same as \frac{1}{5}n.

Three times the number is the same as 3n.

Twice the number plus 42 is the same as 2n + 42.

So, using the information we've gathered so far, we can create the equation that will provide us with n's value.

Equation: \frac{1}{5}n + 3n = 2n + 42

We can use this equation to find n's value.

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