EmilyTorres95
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Hannah went to the school store to buy supplies and spent $16. She bought four more pencils than pens and two fewer erasers than pens. Pens cost $1.25 each, pencils cost $0.55 each, and erasers cost $0.75 each. If x represents the number of pens Hannah bought, write an equation in terms of x that can be used to find how many of each item she bought. Use your equation to determine algebraically how many pens Hannah bought.

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The algebaraic equation required is :

2.55x + 0.7 = 16

The number of pens Hannah bought is 6

If :

x = number of pens

4 more pencils Than pens ; Number of pencils = x + 4

2 fewer erasers than pens ; number of erasers = x - 2

Total amount spent = $16

The total number of items bought is :

(x) + (x + 4) + (x - 2)

Multiplying by the cost of each :

1.25x + 0.55(x+4) + 0.75(x-2)

Hence, Total amount spent can be represented as :

1.25x + 0.55(x+4) + 0.75(x-2) = 16

1.25x + 0.55x + 2.2 + 0.75x - 1.50 = 16

2.55x + 0.7 = 16

The algebraic equation is : 2.55x + 0.7 = 16

The number of pens Hannah bought can be calculated thus :

2.55x + 0.7 = 16

2.55x = 16 - 0.7

2.55x = 15.30

x = 15.30 / 2.55

x = 6

Learn more : https://brainly.com/question/2610134

Answer:

Step-by-step explanation: x = the number of pens Hannah bought

(x + 4) = the number of pencils Hannah bought

(x - 2) = the number of erasers Hannah bought

The equation to solve would be 1.25x + 0.55(x + 4) + 0.75(x - 2) = 16

1.25x + 0.55(x + 4) + 0.75(x - 2) = 16.00

1.25x + 0.55x + 4 * 0.55 + 0.75x - 2 * 0.75 = 16.00

1.25x + 0.55x + 2.20 + 0.75x - 1.50 = 16.00

1.25x + 0.55x + 0.75x = 15.30

2.55x = 15.30

x = 6

Note: if you didn't get a Whole Number, you know that you must've made a mistake. You can't buy part of a pen or pencil or eraser.

x = the number of pens Hannah bought = 6

(x + 4) = the number of pencils Hannah bought = 6 + 4 = 10

(x - 2) = the number of erasers Hannah bought = 6 - 2 = 4

You can check your work: 1.25(6) + 0.55(6 + 4) + 0.75(6 - 2) = 1.25(6) + 0.55(10) + 0.75(4) = 16 (check!)

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