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Jada is going to purchase some writing instruments at the school store, where mechanical pencils cost $\$1$ and pens cost $\$4$ . She can spend up to $\$6$ , but not more. $\newline$ Select the inequality in standard form that describes this situation. Use the given numbers and the following variables. $\newline$ $x =$ the number of mechanical pencils Jada will buy $\newline$ $y =$ the number of pens Jada will buy $\newline$ Choices: $\newline$ (A) $4x + y \leq 6$ $\newline$ (B) $x + 4y \leq 6$ $\newline$ (C) $4x + y < 6$ $\newline$ (D) $x + 4y < 6$

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Write two-variable inequalities: word problems

Full solution

Q. Jada is going to purchase some writing instruments at the school store, where mechanical pencils cost

\$1

and pens cost

\$4

. She can spend up to

\$6

, but not more.

\newline

Select the inequality in standard form that describes this situation. Use the given numbers and the following variables.

\newline

x =

the number of mechanical pencils Jada will buy

\newline

y =

the number of pens Jada will buy

\newline

Choices:

\newline

(A)

4x + y \leq 6

\newline

(B)

x + 4y \leq 6

\newline

(C)

4x + y < 6

\newline

(D)

x + 4y < 6

Calculate Mechanical Pencils Cost: Determine the cost per item for mechanical pencils and pens. Mechanical pencils cost $\$1$ each, so the total cost for mechanical pencils is $1$ times the number of mechanical pencils Jada will buy, which is represented by $x$ . Therefore, the total cost for mechanical pencils is $x$ dollars.
Calculate Pens Cost: Determine the cost per item for pens. Pens cost $\$4$ each, so the total cost for pens is $4$ times the number of pens Jada will buy, which is represented by $y$ . Therefore, the total cost for pens is $4y$ dollars.
Find Total Cost: Combine the costs for mechanical pencils and pens to find the total cost. The total cost is the sum of the cost for mechanical pencils and the cost for pens, which is $x + 4y$ dollars.
Set Spending Limit: Jada can spend up to \$\(6\), but not more. This means the total cost of mechanical pencils and pens must be less than or equal to \$\(6\). Therefore, the inequality that describes this situation is \(x + 4y \leq 6\).

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