Mathematical Process Standards>Applying Mathematics to Everyday Life and Work(TEKS.Math.8.1.A)
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Texas 8th Grade Math › Mathematical Process Standards>Applying Mathematics to Everyday Life and Work(TEKS.Math.8.1.A)
A lawn service charges a 12 dollar travel fee plus 7.50 dollars for each lawn bag of leaves hauled away. If $b$ is the number of bags, which expression gives the total cost in dollars?
$12 + 7.50b$
$12b + 7.50$
$7.50(b - 12)$
$12(7.50 + b)$
Explanation
12 is the fixed travel fee, and 7.50 is the cost for each bag. With $b$ bags, the variable part is $7.50b$, so total cost is $12 + 7.50b$. Option B multiplies the fixed fee by $b$. Option C subtracts the fixed fee inside the bag count. Option D multiplies the fixed fee by the sum, overcounting.
A recipe uses 3 cups of pancake mix to make 12 pancakes. How many cups of mix are needed to make 18 pancakes if the relationship is proportional?
3
5
6
2
Explanation
3 cups corresponds to 12 pancakes. 18 is 1.5 times 12, so the cups also scale by 1.5: $3 \times 1.5 = 4.5$ cups. 3 ignores scaling, 6 doubles instead of multiplying by 1.5, and 1.5 reverses the ratio.
A school fundraiser sold T-shirts for 12 dollars each and wristbands for 4 dollars each. They sold 25 items in all and collected 220 dollars. How many T-shirts did they sell?
10
25
15
5
Explanation
Let $t$ be T-shirts and $w$ be wristbands. Then $t + w = 25$ and $12t + 4w = 220$. Substitute $w = 25 - t$: $12t + 4(25 - t) = 220 \Rightarrow 12t + 100 - 4t = 220 \Rightarrow 8t = 120 \Rightarrow t = 15$. Here, 12 is dollars per T-shirt, 4 is dollars per wristband, 25 is total items, and 220 is total dollars.
A 13-foot ladder leans against a wall so that its base is 5 feet from the wall. How high up the wall does the ladder reach?
12
14
18
8
Explanation
Use the Pythagorean theorem: height $h$ satisfies $h^2 + 5^2 = 13^2$. So $h^2 = 169 - 25 = 144$, giving $h = 12$ feet. 14 uses the wrong operation (adding under the square root), 18 adds the legs, and 8 subtracts lengths instead of using squares.
A reusable water bottle is a cylinder with radius 3 cm and height 20 cm. Which expression gives its volume in cubic centimeters?
$180\pi$
$60\pi$
$9\pi$
$20\pi^2$
Explanation
For a cylinder, $V = \pi r^2 h$. Here $r = 3$ cm so $r^2 = 9$, and $h = 20$ cm. Thus $V = \pi\cdot 9\cdot 20 = 180\pi$. $60\pi$ omits one factor of $r$ ($\pi r h$), $9\pi$ omits the height, and $20\pi^2$ incorrectly squares $\pi$.