Question

Tuli is 10 years younger than Emily. The product of their ages 2 years ago was 39. Let the present age of Emily be A. Which of the following quadratic equations does A satisfy?

Answer 1

$\underline { \blue {At \: present : }}$

$Emily's \: age = A \: [ given ]$

$Tuli's \: age = ( A - 10) \:years$

$\underline { \pink {Two \: years \:ago : }}$

$Emily's \: age = ( A - 2 ) \: years$

$Tuli's \: age = ( A - 10 - 2 ) \:years\\= ( A- 12 ) \: years$

/* According to the problem given */

$\red{ Product\: of \: their \:ages } \green { = 39}$

$\implies (A-2)( A- 12 ) = 39$

$\implies A(A-12) - 2(A-12) - 39 = 0$

$\implies A^{2} - 12A - 2A + 24 - 39 = 0$

$\implies A^{2} - 14A -15 = 0$

Therefore.,

$\red{ Required \: Quadratic \: equation : }\\\green { \: A^{2} - 14A - 15 = 0 }$

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