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Lemur [1.5K]
4 years ago
12

Hero's Challenge: Cars At A StopLight

Mathematics
1 answer:
ruslelena [56]4 years ago
4 0
Summary of the problem: 
Diego=Red
 Ingrid=Sedan
 White then Green
 Rachel then 2 then Minivan 
 SUV then Anton
 Yuna = Green
 Yellow then Convertible
 Rachel then Blue
 Sedan=white 
 Now begin to combine in order:
 1. Rachel
 2 Blue 
 3 Minivan
 Since IngridSedanWhite is followed by YunaGreen, these do not fit as 1,2 or 3 so they must be 4 and 5
 4 IngridSedanWhite
 5 YunaGreen 
 The only place yellow then convertible will fit is in 1 and 2. So:
 1. RachelYellow
 2 ConvertibleBlue
 3 Minivan
 4 IngridSedanWhite
 5 YunaGreen 
 The SUV has to be 1 or 5, but Anton is behind it so the SUV must be #1. So: 
 1. RachelSUVYellow
 2 AntonConvertibleBlue
 3 Minivan
 4 IngridSedanWhite
 5 YunaGreen 
 The only color missing is Red so Diego must be driving the minivan:
 1. RachelSUVYellow
 2 AntonConvertibleBlue
 3 DiegoMinivanRed
 4 IngridSedanWhite
 5 YunaGreen 
 This leaves Yuna to be driving the green pickup truck.
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On Naomi's cell phone plan, the amount she pays each month for international text messages is proportional to the number of inte
Lostsunrise [7]

A) The constant of proportionality in this proportional relationship is k = \frac{y}{x}

B) The equation to represent this proportional relationship is y = 0.2x

<h3><u>Solution:</u></h3>

Given that,

The amount Naomi pays each month for international text messages is proportional to the number of international texts she sends that month

Therefore,

This is a direct variation proportion

\text{ amount Naomi pays each month } \propto \text{ number of international texts she sends that month}

Let "y" be the amount that Naomi pays each month

Let "x" be the number of international texts she sends that month

Therefore,

y \propto x

y = kx -------- eqn 1

Where, "k" is the constant of proportionality

Thus the constant of proportionality in this proportional relationship is:

k = \frac{y}{x}

<em><u>Last month, she paid $3.20 for 16 international texts</u></em>

Therefore,

y = 3.20

x = 16

Thus from eqn 1,

3.20 = k \times 16\\\\k = \frac{3.20}{16}\\\\k = 0.2

Substitute k = 0.2 in eqn 1

y = 0.2x

The equation would then be y = 0.2x

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