Question

Geoffrey is trying to earn $50 to buy a video game. He has saved $14.25. He earns $3.75 per hour cleaning windows with his uncle and he earns $6.50 per hour working at the grocery store. Can Fred buy the video game if he works with his uncle for 3 hours and at the grocery store for 4 hours? Use the inequality 3.75y + 6.50z + 14.25 ≥ 50. Yes, because the total will be $51.50. Yes, because the total will be $60.25. No, because the total will be $24.50. No, because the total will be $37.25.

Answer 1

SOLUTION

TO CHOOSE THE CORRECT OPTION

Geoffrey is trying to earn $50 to buy a video game. He has saved $14.25. He earns $3.75 per hour cleaning windows with his uncle and he earns $6.50 per hour working at the grocery store. Can Fred buy the video game if he works with his uncle for 3 hours and at the grocery store for 4 hours?

Use the inequality 3.75y + 6.50z + 14.25 ≥ 50.

• Yes, because the total will be $51.50.

• Yes, because the total will be $60.25.

• No, because the total will be $24.50.

• No, because the total will be $37.25.

EVALUATION

Verification of Inequality

Here it is given that Geoffrey is trying to earn $50 to buy a video game.

He has saved $14.25.

He earns $3.75 per hour cleaning windows with his uncle and he earns $6.50 per hour working at the grocery store

Let he spends y hour for cleaning windows with his uncle and spends z hour at the grocery store

So total amount = 3.75y + 6.50z + 14.25

In order to buy the video game it must be greater than equal to 50

Hence the correct inequality is

3.75y + 6.50z + 14.25 ≥ 50

CHECKING FOR SOLUTION

Taking x = 3 & y = 4 we have

LHS

= 3.75y + 6.50z + 14.25

= 3.75 × 3 + 6.50 × 4 + 14.25

= 11.25 + 26 + 14.25

= 51.50

RHS = 50

Clearly 51.50 > 50

So x = 3 & y = 4 is one valid solution of

3.75y + 6.50z + 14.25 ≥ 50.

FINAL ANSWER

Hence the correct option is

Yes, because the total will be $ 51.50

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