WORD+PROBLEMS+CHAPTER+2

C H A P T E R 2 W O R D P R O B <span style="FONT-SIZE: 180%; COLOR: #06ff65; FONT-FAMILY: 'Comic Sans MS', Courier, monospace">L <span style="FONT-SIZE: 180%; COLOR: #10ff65; FONT-FAMILY: 'Comic Sans MS', Courier, monospace">E <span style="FONT-SIZE: 180%; COLOR: #15ff65; FONT-FAMILY: 'Comic Sans MS', Courier, monospace">M <span style="FONT-SIZE: 180%; COLOR: #20ff65; FONT-FAMILY: 'Comic Sans MS', Courier, monospace">S

<span style="FONT-SIZE: 60%; COLOR: #000000; FONT-FAMILY: Tahoma, Geneva, sans-serif">Word Problems from Chapter 2 are similar to those from chapter 1, but have a key difference: They deal with inequalities.

Expressing inequalities as an answer to a problem is easy:

There were at least 50 people at the shop: x <span style="FONT-SIZE: 11pt; LINE-HEIGHT: 115%; FONT-FAMILY: 'Tahoma','sans-serif'; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-ansi-language: EN-US; mso-fareast-language: EN-US; mso-bidi-language: AR-SA">≥ 50 Frank makes at most $35 an hour: x <span style="FONT-SIZE: 11pt; LINE-HEIGHT: 115%; FONT-FAMILY: 'Tahoma','sans-serif'; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-ansi-language: EN-US; mso-fareast-language: EN-US; mso-bidi-language: AR-SA">≤ 35 There were more than 80 fish in the aquarium: x > 80 There were 12 people at the market. There were less than that at the bakery. x < 12

Now, some actual problems: <span style="FONT-SIZE: 110%; COLOR: #580909; FONT-FAMILY: Tahoma, Geneva, sans-serif"> 1. A store is charged 1 dollar per baseball and a 20 dollar delivery charge. How many baseballs must they sell to make at least $200 in profit if they sell the baseballs for $2.25?

Remember, Income - Cost = Profit

So Income= 2.25x, and Cost is 20 (delivery charge) + x (cost/baseball). So the profit would be 2.25x - (20 + x).

So we set up an inequality so there is at least $200 in profit:

2.25x - (20 + x) <span style="FONT-SIZE: 11pt; LINE-HEIGHT: 115%; FONT-FAMILY: 'Tahoma','sans-serif'; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-ansi-language: EN-US; mso-fareast-language: EN-US; mso-bidi-language: AR-SA">≥ 200 Simplify:

1.25x - 20 <span style="FONT-SIZE: 11pt; LINE-HEIGHT: 115%; FONT-FAMILY: 'Tahoma','sans-serif'; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-ansi-language: EN-US; mso-fareast-language: EN-US; mso-bidi-language: AR-SA">≥ 200 1.25x <span style="FONT-SIZE: 11pt; LINE-HEIGHT: 115%; FONT-FAMILY: 'Tahoma','sans-serif'; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-ansi-language: EN-US; mso-fareast-language: EN-US; mso-bidi-language: AR-SA">≥ 220

x <span style="FONT-SIZE: 11pt; LINE-HEIGHT: 115%; FONT-FAMILY: 'Tahoma','sans-serif'; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-ansi-language: EN-US; mso-fareast-language: EN-US; mso-bidi-language: AR-SA">≥ 176. So the store must sell at least 176 baseballs to make a profit of $200

<span style="FONT-SIZE: 110%; COLOR: #5e0808; FONT-FAMILY: Tahoma, Geneva, sans-serif"> 2. A square, pentagon, and a octagon all have equal sides. If the sum of the perimeters of the square and the pentagon is no more than 33 centimeters more than half the perimeter of the octagon, what is the maximum length of each side?

Set up the problem:

4x + 5x <span style="FONT-SIZE: 11pt; LINE-HEIGHT: 115%; FONT-FAMILY: 'Tahoma','sans-serif'; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-ansi-language: EN-US; mso-fareast-language: EN-US; mso-bidi-language: AR-SA">≤ 33 + 1/2(8x)

And Solve: 9x <span style="FONT-SIZE: 11pt; LINE-HEIGHT: 115%; FONT-FAMILY: 'Tahoma','sans-serif'; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-ansi-language: EN-US; mso-fareast-language: EN-US; mso-bidi-language: AR-SA">≤ 33 + 4x 5x <span style="FONT-SIZE: 11pt; LINE-HEIGHT: 115%; FONT-FAMILY: 'Tahoma','sans-serif'; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-ansi-language: EN-US; mso-fareast-language: EN-US; mso-bidi-language: AR-SA">≤ 33 x <span style="FONT-SIZE: 11pt; LINE-HEIGHT: 115%; FONT-FAMILY: 'Tahoma','sans-serif'; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-ansi-language: EN-US; mso-fareast-language: EN-US; mso-bidi-language: AR-SA">≤ 6.6 The maximum length of each side is 6.6 cm.

<span style="FONT-SIZE: 110%; COLOR: #580909; FONT-FAMILY: Tahoma, Geneva, sans-serif"> 3. Find all sets of 4 consecutive integers that are divisible by 4, whose sum is between 160 and 200.

Set up the problem:

160 < x + x+4 + x+8 + x+12 < 200

And solve:

160 < 4x + 24 < 200

136 < 4x < 176

34 < x < 44

And since x must be divisible by 4, only 36 and 40 will work. So the sets of numbers would be:

36,40,44,48

or

40,44,48,52

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