Question

Marcus can spend no more than $\$120$ on jeans and shirts for school. He buys $3$ pairs of jeans at $\$32$ each. If $x$ represents the dollar amount he can spend on shirts, which of the following inequalities could be used to determine the possible values for $x$?

• A. $3\left(32\right)-x\le 120$
• B. $3\left(32\right)-x\ge 120$
• C. $3\left(32\right)+x\le 120$
• D. $3\left(32\right)+x\ge 120$
• E. $x\le 3\left(32\right)$

Answer 1

The correct option is C $3\left(32\right)+x\le 120$

Given: Amount that Marcus can spend on jeans and shirts is no more than 120$

Formally, amount that Marcus can spend on jeans and shirts in dollars $\le$ $120$

As Marcus buys $3$ pairs of jeans at 32$ each,

Amount Marcus spent on jeans in dollars $=$ $3.\left(32\right)$

Amount Marcus can spend on shirts in dollars $=$ $x$

From above, amount that Marcus can spend on jeans and shirts in dollars $=$ Amount Marcus spent on jeans in dollars $+$ Amount Marcus can spend on shirts in dollars

$=$ $3.\left(32\right)$ $+$ $x$

As amount that Marcus can spend on jeans and shirts in dollars $\le$ $120$

$\Rightarrow 3.\left(32\right)$ $+$ $x$ $\le$ $120$

Therefore, the possible values of ${}^{\prime }{x}^{\prime }$ can be determined by $3.\left(32\right)$ $+$ $x$ $\le$ $120$.