Question

Aflați x stiind ca: a) x×(1+2+3+...+100)=60.000

b) (1+2+3+...+100):x=101


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Answer 1

$a)x(1 + 2 + 3 + ... + 100) = 60000$

$x \times \frac{100(100 + 1)}{2} = 60000$

$x \times \frac{100 \times 101}{2} = 60000$

$x \times 50 \times 101 = 60000 \: | \div 50$

$101x = 1200$

$x = \frac{1200}{101}$

$b)(1 + 2 + 3 + ... + 100) \div x = 101$

$\frac{100(100 + 1)}{2} \div x = 101$

$\frac{100 \times 101}{2} \div x = 101$

$\frac{50 \times 101}{x} = 101 \: | \times x$

$101x = 50 \times 101 \: | \div 101$

$x = 50$