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Oscar is buying soda and juice for a party and wants to spend no more than $\$46$ . Soda costs $\$2$ per bottle, and juice costs $\$1$ per bottle. $\newline$ Select the inequality in standard form that describes this situation. Use the given numbers and the following variables. $\newline$ $x =$ the number of bottles of soda $\newline$ $y =$ the number of bottles of juice $\newline$ Choices: $\newline$ (A) $2 + x + 1 + y \leq 46$ $\newline$ (B) $2x + y \leq 46$ $\newline$ (C) $x + 2y \leq 46$ $\newline$ (D) $1 + x + 2 + y \leq 46$

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Write a linear inequality: word problems

Full solution

Q. Oscar is buying soda and juice for a party and wants to spend no more than

\$46

. Soda costs

\$2

per bottle, and juice costs

\$1

per bottle.

\newline

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

\newline

x =

the number of bottles of soda

\newline

y =

the number of bottles of juice

\newline

Choices:

\newline

(A)

2 + x + 1 + y \leq 46

\newline

(B)

2x + y \leq 46

\newline

(C)

x + 2y \leq 46

\newline

(D)

1 + x + 2 + y \leq 46

Define Variables: Oscar is buying soda and juice for a party and wants to spend no more than $\$46$ . We need to find the inequality that represents this situation using the given variables and prices.
Calculate Total Cost: Let's define the variables: $\newline$ $x =$ the number of bottles of soda $\newline$ $y =$ the number of bottles of juice $\newline$ The cost of soda is $\$2$ per bottle, and the cost of juice is $\$1$ per bottle.
Formulate Inequality: Now, we calculate the total cost for $x$ bottles of soda and $y$ bottles of juice. $\newline$ Total cost of soda = $2 \times x$ $\newline$ Total cost of juice = $1 \times y$ $\newline$ Total cost = Total cost of soda + Total cost of juice $\newline$ Total cost = $2x + y$
Formulate Inequality: Now, we calculate the total cost for $x$ bottles of soda and $y$ bottles of juice. $\newline$ Total cost of soda = $2 \times x$ $\newline$ Total cost of juice = $1 \times y$ $\newline$ Total cost = Total cost of soda + Total cost of juice $\newline$ Total cost = $2x + y$ Since Oscar wants to spend no more than $\$46$ , the total cost must be less than or equal to $\$46$ . $\newline$ So, the inequality that represents this situation is: $\newline$ $2x + y \leq 46$

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