Answer to Question #237945 in Algebra for Ahood

Question

a baker in 70 minutes iced 40 cupcakes and in 49 minutes iced 28 cupcakes. what is the constant of proposinalty

Answer 1

Suppose $y=minutes$ and $x=cupcakes$

So $y=kx+b$

Put $(40,70)$ and $(28, 49)$ into equation $y=kx+b$

So, $70=40k+b$

$49=28k+b$

Dividing equation: $70=40k+b$ by 10 we get $7=4k+\frac{1}{10}b$

so $7-4k=\frac{1}{10}b$

Dividing equation: $49=28+b$ by 7 we get $7=4k+\frac{1}{7}b$

so $7-4k=\frac{1}{7}b$

So $\frac{1}{10}b=\frac{1}{7}b$

So $b=0$

Substitute b into equation: $70=40k+b$

$70=40k$

$k=\frac{70}{40}=\frac{7}{4}$

$k=1.75$

Thus, the constant of proportionality is 1.75.