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1. The difference of 2 numbers is 60, with the ratio of 9 to 7. What are the numbers.?
need solution po


Sagot :

Answer:

Let x - the large number

y - the small number

Equations:

[tex]x - y = 60 \: \: \: \: \: \: \: [E1]\\ \frac{x}{y} = \frac{9}{7} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: [E2][/tex]

Solve x in term of y of [E1] and substitute to corresponding x of [E2].

[tex]x - y = 60 \: \: \: \: = > \: \: \: x = y + 60[/tex]

[tex] \frac{x}{y} = \frac{9}{7} \: \: \: = > \: \: \: \frac{y + 60}{y} = \frac{9}{7} [/tex]

[tex]7(y + 60) = 9(y) \\ 7y + 420 = 9y \\ 420 = 9y - 7y \\ 420 = 2y \\ y = \frac{420}{2} \\ y = 210[/tex]

[tex]x = y + 60 \\ x = 210 + 60 \\ x = 270[/tex]

Therefore, 210 and 270 are the numbers.