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marshall27 [118]
2 years ago
13

One apple and three oranges cost $5.10 and another 5 oranges and one Apple cost $7.50 what is the price of one apple and one ora

nge
Mathematics
1 answer:
alekssr [168]2 years ago
4 0

Answer:

$2.7

Step-by-step explanation:

Let the price of one apple be x

and the price of one orange y

Hence ;

One apple and 3 oranges would cost:

x + 3×y = $5.10----------------------------(1)

One apple and 5 oranges would cost;

x + 5×y = $7.50--------------------------(2)

Subtracting eqn (1) from (2), we have :

x-x + 5y -3y = 7.5- 5.1

2y = 2.4

y = $1.2

From eqn(1)

x + 3y = $5.10

x= $5.10-3($1.2) = $5.10-$3.6 = $1.5

Hence x=$1.5 and y= $1.2

We are required to find the cost of one apple and one orange, hence :

x+y = $1.5+$1.2= $2.7

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Answer:

Husband:

The husband will have 16.35 mg of caffeine in his body at 7 pm.

Woman:

The pregnant woman will have 51.33 mg of caffeine in her body at 7 pm.

Step-by-step explanation:

The amount of caffeine in the body can be modeled by the following equation:

C(t) = C(0)e^{rt}

In which C(t) is the amount of caffeine t hours after 8 am, C(0) is how much coffee they took and r is the rate the the amount of caffeine decreases in their bodies.

110 mg of caffeine at 8 am,

So C(0) = 110

Husband

Half life of 4 hours. So

C(4) = 0.5C(0) = 0.5*110 = 55

C(t) = C(0)e^{rt}

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e^{4r} = 0.5

Applying ln to both sides

\ln{e^{4r}} = \ln{0.5}

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r = \frac{\ln{0.5}}{4}

r = -0.1733

So for the husband

C(t) = 110e^{-0.1733t}

At 7 pm

7 pm is 11 hours after 8 am, so this is C(11)

C(t) = 110e^{-0.1733t}

C(11) = 110e^{-0.1733*11} = 16.35

The husband will have 16.35 mg of caffeine in his body at 7 pm.

Pregnant woman

Half life of 10 hours. So

C(10) = 0.5C(0) = 0.5*110 = 55

C(t) = C(0)e^{rt}

55 = 110e^{10}

e^{10r} = 0.5

Applying ln to both sides

\ln{e^{10r}} = \ln{0.5}

10r = \ln{0.5}

r = \frac{\ln{0.5}}{10}

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At 7 pm

7 pm is 11 hours after 8 am, so this is C(11)

C(t) = 110e^{-0.0693t}

C(11) = 110e^{-0.0693*11} = 51.33

The pregnant woman will have 51.33 mg of caffeine in her body at 7 pm.

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