6 and 9 are two given numbers .
i) What should be added to these numbers to get a ratio of 5:6 ?
ii) What should be subtracted from these numbers to get a ratio of 1:2?

Question

6 and 9 are two given numbers .
i) What should be added to these numbers to get a ratio of 5:6 ?
ii) What should be subtracted from these numbers to get a ratio of 1:2?

Accepted Answer

∻Solution by Steps∻ ‖ step 1 ⋮ To find what should be added to the numbers 6 and 9 to get a ratio of 5:6, we set up the equation $\frac{6 + x}{9 + x} = \frac{5}{6}$. ‖ ‖ step 2 ⋮ Cross-multiplying to solve for $x$, we get $6(6 + x) = 5(9 + x)$. ‖ ‖ step 3 ⋮ Expanding both sides, we have $36 + 6x = 45 + 5x$. ‖ ‖ step 4 ⋮ Subtracting $5x$ from both sides, we get $36 + x = 45$. ‖ ‖ step 5 ⋮ Subtracting 36 from both sides, we find $x = 9$. ‖ ∻Answer∻ ⚹ To get a ratio of 5:6, 9 should be added to both numbers. ⚹ ∻Key Concept∻ ⚹Ratio Adjustment⚹ ∻Explanation∻ ⚹To adjust the ratio of two numbers, we set up a proportion and solve for the variable representing the adjustment.⚹ ∻Solution by Steps∻ ‖ step 1 ⋮ To find what should be subtracted from the numbers 6 and 9 to get a ratio of 1:2, we set up the equation $\frac{6 - x}{9 - x} = \frac{1}{2}$. ‖ ‖ step 2 ⋮ Cross-multiplying to solve for $x$, we get $2(6 - x) = 1(9 - x)$. ‖ ‖ step 3 ⋮ Expanding both sides, we have $12 - 2x = 9 - x$. ‖ ‖ step 4 ⋮ Adding $2x$ to both sides, we get $12 = 9 + x$. ‖ ‖ step 5 ⋮ Subtracting 9 from both sides, we find $x = 3$. ‖ ∻Answer∻ ⚹ To get a ratio of 1:2, 3 should be subtracted from both numbers. ⚹ ∻Key Concept∻ ⚹Ratio Adjustment⚹ ∻Explanation∻ ⚹To adjust the ratio of two numbers, we set up a proportion and solve for the variable representing the adjustment.⚹◊What is the formula to find the ratio between two numbers?⍭ Generate me a similar question◊

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