# On a linear X temperature scale, water freezes at &#x2212;<!-- − --> 125.0 0 </

On a linear X temperature scale, water freezes at $-{125.0}^{0}X$ and boils at ${360.0}^{0}X$. On a linear Y scale, water freezes at $-{70.00}^{0}Y$ and boils at $-{30.00}^{0}Y$. A temperature of ${50.00}^{0}Y$ corresponds to what temperature on the X scale?
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Gary Salinas
If you rearrange your equation to solve for Y,
$Y=\left(X+125\right)\frac{-30+70}{360+125}-70$
This reduces to
$Y=\frac{8X-5790}{97}=0.08247X+59.6907\approx 0.08X-60$
which is about what the textbook obtains.
The difference in values you are getting is completely due to the approximation that the solution manual uses. If you use the exact values, as you did, you will indeed get 1330. If you use the approximate values as the solution manual did, then you will indeed get 1375.