What would be the highest value of X in the given equation?
7X5 + 2Y3 + 8Z7 = 1805
Given:
The equation is:
7X5 + 2Y3 + 8Z7 = 1805
Solution:
Let’s write the numbers with variables as digits:
7X5 = 700 + 10×X + 5
2Y3 = 200 + 10×Y + 3
8Z7 = 800 + 10×Z + 7
Total = 700 + 10X + 5 + 200 + 10Y + 3 + 800 + 10Z + 7 = 1805
Combine constants:
(700 + 200 + 800) + (5 + 3 + 7) + (10X + 10Y + 10Z) = 1805
1700 + 15 + 10(X + Y + Z) = 1805
1715 + 10(X + Y + Z) = 1805
10(X + Y + Z) = 90
X + Y + Z = 9
To maximize X, minimize Y + Z.
Minimum sum of Y + Z = 0
X = 9
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