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Hyun Yong wants to donate more than
$5000 in laptops and bicycles. Each laptop that he donates is worth
$200, and each bicycle that he donates is worth
$100.
Write an inequality that represents the number of laptops
(L) and bicycles
(B) that Hyun Yong should donate to achieve his goal.

Hyun Yong wants to donate more than $(5000$ in laptops and bicycles. Each laptop that he donates is worth $)200$ , and each bicycle that he donates is worth $\$100$ . Write an inequality that represents the number of laptops $L$ and bicycles $B$ that Hyun Yong should donate to achieve his goal.

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Modeling with linear inequalities

Full solution

Q. Hyun Yong wants to donate more than

(5000

in laptops and bicycles. Each laptop that he donates is worth

)200

, and each bicycle that he donates is worth

\$100

. Write an inequality that represents the number of laptops

L

and bicycles

B

that Hyun Yong should donate to achieve his goal.

Define Total Value Function: Let's define the total value of the laptops and bicycles that Hyun Yong donates as $T$ . The value of each laptop is $\$200$ , and the value of each bicycle is $\$100$ . We can express $T$ as a function of the number of laptops ( $L$ ) and bicycles ( $B$ ) he donates. $\newline$ $T = 200L + 100B$
Set Donation Value Constraint: Hyun Yong wants to donate more than $\$5000$ , so the total value $T$ must be greater than $\$5000$ . Therefore, the inequality that represents this situation is: 200L + 100B > 5000
Check Initial Values: We should check if the inequality makes sense with the values given. If Hyun Yong donates $0$ laptops and $0$ bicycles, the total value would be $\$0$ , which is not greater than $\$5000$ . This is consistent with the inequality since $0$ does not satisfy the inequality 200L + 100B > 5000.

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