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Harry is saving up to buy a smartphone that is selling for [tex]\$ 510[/tex]. He has [tex]\$ 220[/tex] in his bank account and expects a sum of money for his birthday next month.

If the amount he is to receive for his birthday is represented by [tex]x[/tex], which of the following inequalities models the situation where he is able to afford the smartphone?

A. [tex]x + 220 \geq 510[/tex]
B. [tex]x - 220 \geq 510[/tex]
C. [tex]x + 220 \leq 510[/tex]
D. [tex]x - 220 \leq 510[/tex]

Answer :

To determine how much money Harry needs to receive for his birthday in order to afford the smartphone, follow these steps:

1. Harry already has \[tex]$220 in his bank account. The smartphone costs \$[/tex]510. Therefore, the total amount of money Harry will have is the sum of his current money and the birthday money, which is represented by [tex]$x$[/tex].

2. For Harry to be able to afford the smartphone, his total money must be at least \[tex]$510. This relationship can be written as the inequality:
$[/tex][tex]$
x + 220 \geq 510.
$[/tex][tex]$

3. Next, subtract 220 from both sides of the inequality to determine the minimum birthday money he needs:
$[/tex][tex]$
x \geq 510 - 220,
$[/tex][tex]$
which simplifies to:
$[/tex][tex]$
x \geq 290.
$[/tex][tex]$

Thus, the correct inequality that models the situation is
$[/tex][tex]$
x + 220 \geq 510.
$[/tex][tex]$

In summary, the birthday sum $[/tex]x[tex]$ must be at least \$[/tex]290, so the correct option is the first one.

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