Question

write an algebraic expression for each of the given quantities.
minh gives baseball cards to four of his friends. he gives chloe 3 cards less than he gives liam. he gives elijah 7 cards more than he gives chloe. he gives mia twice as many as
how many cards does minh give to each friend should he give out a total of 6 times what chloe has? let ( x ) represent the number of cards given to liam.
→ enter the answer in each space provided. use numbers instead of words.

expression	cards given to chloe	cards given to elijah	cards given to mia

answer the question by writing and solving an equation.
→ enter the answer in each space provided. use numbers instead of words.
equation

minh gives (square) cards to liam, (square) cards to chloe, (square) cards to elijah, and (square) cards to mia.

Explanation:

Step1: Define variables & expressions

Let $x$ = cards given to Liam.

• Cards to Chloe: $x-3$
• Cards to Elijah: $(x-3)+7 = x+4$
• Cards to Mia: $2(x+4) = 2x+8$

Step2: Set up total cards equation

Total cards = 6 times Chloe's cards:
$$x + (x-3) + (x+4) + (2x+8) = 6(x-3)$$

Step3: Simplify left side

Combine like terms:
$$x+x-3+x+4+2x+8 = 5x+9$$

Step4: Simplify right side

Distribute the 6:
$$6(x-3) = 6x-18$$

Step5: Solve for $x$

Rearrange to isolate $x$:
$$5x+9 = 6x-18$$
$$9+18 = 6x-5x$$
$$x=27$$

Step6: Calculate each friend's cards

• Chloe: $27-3=24$
• Elijah: $27+4=31$
• Mia: $2(31)=62$

Answer:

Expressions:

Cards Given to Chloe: $x-3$
Cards Given to Elijah: $x+4$
Cards Given to Mia: $2x+8$

Final Card Counts:

Minh gives $\boldsymbol{27}$ cards to Liam, $\boldsymbol{24}$ cards to Chloe, $\boldsymbol{31}$ cards to Elijah, and $\boldsymbol{62}$ cards to Mia.

Equation:

$$5x+9=6x-18$$