Two temperature scales A and B are related by | vedclass

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Question

(C) Given the relationship between the two temperature scales is $\frac{A-42}{110} = \frac{B-72}{220}$.To find the temperature where both scales have

Vedclass · Accepted Answer

$+12^{\circ}$

Vedclass · Answer

(C) Given the relationship between the two temperature scales is $\frac{A-42}{110} = \frac{B-72}{220}$.To find the temperature where both scales have the same reading, we set $A = B = T$.Substituting $T$ into the equation: $\frac{T-42}{110} = \frac{T-72}{220}$.Simplifying the equation by dividing the denominators by $110$: $\frac{T-42}{1} = \frac{T-72}{2}$.Cross-multiplying gives: $2(T-42) = T-72$.Expanding the terms: $2T - 84 = T - 72$.Rearranging to solve for $T$: $2T - T = 84 - 72$.Thus, $T = 12$.Therefore, the two scales have the same reading at $12^{\circ}$.

Two temperature scales $A$ and $B$ are related by $\frac{A-42}{110}=\frac{B-72}{220}$. At which temperature do the two scales have the same reading?

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