Question

If a:b=3:4 find the value of 15a+9b:16a+5b​

Answer 1

• 81 : 68

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Explanation:

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`{\longrightarrow \: \sf \: Let \: \: a : b\: = 3: 4 = (a)/(b) \: = \: (3)/(4) = k}`

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Therefore,

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`\dashrightarrow \qquad \sf \: a = 3k`

`\dashrightarrow \qquad \sf \: b = 4k`

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Now, Substituting the values :

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`\longrightarrow \qquad \sf \: 15a+9b:16a+5b`

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`\longrightarrow \qquad \sf \: (15(3k)+9(4k))/(16(3k)+5(4k))`

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`\longrightarrow \qquad \sf \: (45k+36k)/(48k+20k)`

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`\longrightarrow \qquad \sf \: (81k)/(68k)`

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`\longrightarrow \qquad \sf \: \frac{81 \cancel{k}}{68 \cancel{k}}`

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`\longrightarrow \qquad \sf \: (81)/(68)`

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`\longrightarrow \qquad \bf \: {81} : {68}`

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Therefore ,

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`{ \pmb{ \sf{\longrightarrow \qquad \: 15a+9b:16a+5b = 81 : 68}}}`

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