Proportionality>Solving Problems Involving Direct Variation(TEKS.Math.8.5.E)
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Texas 8th Grade Math › Proportionality>Solving Problems Involving Direct Variation(TEKS.Math.8.5.E)
The total cost $C$ varies directly with the number of notebooks $n$. If $C=18$ when $n=6$, which equation represents this direct variation?
$C=\frac{n}{3}$
$n=3C$
$C=18n+6$
$C=3n$
Explanation
For direct variation, $C=kn$. Find $k=\frac{C}{n}=\frac{18}{6}=3$, so $C=3n$. The other options invert the relationship, add a nonzero intercept, or solve for the wrong variable.
The number of servings $s$ varies directly with the cups of flour $f$. If $s=12$ when $f=3$, how many servings are made when $f=7$?
18
21
84
28
Explanation
Since $s=kf$, find $k=\frac{12}{3}=4$. Then $s=4\cdot 7=28$. The distractors come from adding instead of multiplying, using $3$ servings per cup, or multiplying $12\cdot 7$.