This word problems worksheet helps students practice applying math concepts to everyday situations involving money, time, and measurements.

Here are the step-by-step solutions for each problem on the worksheet.

Problem 1

Goal: Find the cost of 1 hockey puck.

Let $p$ be the cost of a puck and $s$ be the cost of a stick.
From the first sentence: $5p + 3s = 23$
From the second sentence: $2p + 1s = 20$

We can solve this by substitution. From the second equation, we know that 1 stick costs $20 - 2p$.
Now, substitute that into the first equation where $s$ is:
$5p + 3(20 - 2p) = 23$
$5p + 60 - 6p = 23$
$-1p + 60 = 23$
Subtract 60 from both sides:
$-1p = -37$
$p = 37$

So, one hockey puck costs $37.
*(Check: If a puck is $\$37$, a stick is $20 - (2 \times 37) = 20 - 74 = -\$54$. While negative money is impossible in real life, mathematically this is the correct answer derived from the numbers provided in the problem.)*

Problem 2

Goal: Find Jan's age.

Let $J$ be Jan's age and $B$ be her brother's age.
1. "Her brother Jack will be 2 years from being twice as old as his sister Jan."
Equation: $B + 2 = 2J$
2. "The sum of Jack's age and three times Jen's age is 66." (Note: The problem likely means "Jan" instead of "Jen").
Equation: $B + 3J = 66$

From the first equation, we can isolate $B$:
$B = 2J - 2$

Substitute this into the second equation:
$(2J - 2) + 3J = 66$
Combine the $J$'s:
$5J - 2 = 66$
Add 2 to both sides:
$5J = 68$
Divide by 5:
$J = 13.6$

Jan is 13.6 years old (or 13 years and roughly 7 months).

Problem 3

Goal: Find how many pounds of vanilla fudge were sold.

First, calculate the money made from chocolate fudge:
40 pounds $\times$ $\$2.15$/pound = $\$86.00$

Next, find out how much money came from vanilla fudge by subtracting the chocolate total from the class total:
$\$158.20$ (total) - $\$86.00$ (chocolate) = $\$72.20$ (vanilla total)

Finally, divide the vanilla total by the price per pound to find the weight:
$\$72.20 / \$3.90$ per pound $\approx$ 18.51 pounds.

Problem 4

Goal: Find how many hours before the cars pass each other.

This is a relative speed problem. Since they are driving toward each other, you add their speeds together to see how fast the gap between them is closing.
Speed 1: 1025 mph
Speed 2: 53 mph
Combined Speed: $1025 + 53 = 1078$ mph

Total Distance: 45 miles

Time = Distance / Speed
Time = $45 / 1078$
Time $\approx$ 0.0417 hours (which is about 2.5 minutes).

Problem 5

Goal: Calculate how much Dana needs to spend.

Dana needs 300 pickets total. She already has:
32 red + 26 green + 9 yellow + 0 blue = 67 pickets.

She needs to buy: $300 - 67 = 233$ pickets.
She wants equal amounts of each of the 4 colors.
$233 / 4 = 58.25$. Since she can't buy partial bulbs, she must buy 59 of each color to have enough.
Total bulbs to buy: $59 \times 4 = 236$ bulbs.

Cost calculation:
Base price is 25 cents ($\$0.25$) per bulb.
Since she is buying more than 50 bulbs, she gets a 20% discount.
Discounted price per bulb: $\$0.25 \times (1 - 0.20) = \$0.25 \times 0.80 = \$0.20$.

Total Cost:
236 bulbs $\times$ $\$0.20$ = $47.20

Final Answer:
1. $37
2. 13.6 years old
3. ~18.51 pounds
4. ~0.042 hours
5. $47.20