Algebra Worksheet-4 from Cuemath with problems on simplifying expressions, translating phrases, solving a riddle, and calculating team costs.

Let's solve each problem step by step from the Algebra Worksheet-4.

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1. Find the sum: (5x + 4 - 2y) + (2y - 7 + 3x)

We need to combine like terms.

Start by removing parentheses:

$$
5x + 4 - 2y + 2y - 7 + 3x
$$

Now group like terms:

- $5x + 3x = 8x$
- $-2y + 2y = 0$
- $4 - 7 = -3$

So, the simplified expression is:

$$
\boxed{8x - 3}
$$

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2. Translate the verbal phrase into an algebraic expression:

> "One-third of x increased by four-fifths is equal to a quarter."

Break it down:

- "One-third of x" → $\frac{1}{3}x$
- "increased by four-fifths" → $\frac{1}{3}x + \frac{4}{5}$
- "is equal to a quarter" → $= \frac{1}{4}$

So, the equation is:

$$
\frac{1}{3}x + \frac{4}{5} = \frac{1}{4}
$$

✔ This is the algebraic expression.

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3. Solve the riddle:

We have three equations using symbols for basketballs and footballs.

Let:
- Basketball = $ b $
- Football = $ f $

#### Equation 1:
$$
b + b + b = 15 \Rightarrow 3b = 15 \Rightarrow b = 5
$$

#### Equation 2:
$$
f - 4b = -5
$$

Substitute $ b = 5 $:

$$
f - 4(5) = -5 \Rightarrow f - 20 = -5 \Rightarrow f = 15
$$

#### Equation 3:
$$
b + b + f = ?
$$

Substitute values:

$$
5 + 5 + 15 = \boxed{25}
$$

✔ So, the answer is 25.

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4. Write and simplify an expression that represents the total cost (in dollars) of buying the items shown for each member of a varsity team? (1 T-shirt and a pair of socks per member)

Given:
- T-shirt = \$10
- Socks = \$x per pair

Each member gets:
- 1 T-shirt → \$10
- 1 pair of socks → \$x

So, cost per member = $10 + x$

If there are n members on the team, then total cost = $ n(10 + x) $

But the question says: *"for each member"* — so unless the number of members is given, we assume we're writing an expression per member or in general.

However, since it says “the total cost... for each member”, but asks for total cost, likely they want the expression in terms of number of members, say $ n $.

But the image doesn't specify how many members. So, let’s assume there are $ n $ members.

Then total cost = $ n \times (10 + x) $

Simplified:

$$
\boxed{n(10 + x)}
$$

Alternatively, if the question just wants the cost per member, it would be $10 + x$. But since it says total cost for all members, and no number is given, the most accurate answer is:

$$
\boxed{n(10 + x)} \quad \text{(where } n \text{ is the number of team members)}
$$

But if the worksheet expects only a simplified expression without variables for count, maybe it assumes one member? But that contradicts "total cost".

Wait — re-read:
> "the total cost (in dollars) of buying the items shown for each member"

This phrasing is ambiguous. But logically, if you’re buying for each member, and you don’t know how many, the best expression is:

$$
\boxed{10 + x} \quad \text{per member}
$$

But again, it says total cost.

So likely, the intended answer is:

> Let $ n $ be the number of members.

Total cost = $ n \times (10 + x) = \boxed{n(10 + x)} $

If no variable is used, perhaps they expect:

$$
\boxed{10n + nx}
$$

Either form is acceptable, but $ n(10 + x) $ is simplified.

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✔ Final Answers:

1. $ \boxed{8x - 3} $
2. $ \boxed{\frac{1}{3}x + \frac{4}{5} = \frac{1}{4}} $
3. $ \boxed{25} $
4. $ \boxed{n(10 + x)} $ or $ \boxed{10n + nx} $ (where $ n $ = number of team members)

Let me know if you'd like a version with specific numbers!