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Rina8888 [55]
3 years ago
6

Five friends bought admission tickets the museum and a box lunch.the cost of each admission ticket was $11.75.each box lunch cos

t $5.write two equivalent expressions and then find the total cost.
Mathematics
1 answer:
slega [8]3 years ago
4 0
Cost of the admission tickets: 11.75x

Cost of the box lunch: 5x

Expressions to find the total cost = (1) ....... 11.75x + 5x

That is equivalent to: (2) .......... (11.75 + 5)x = 16.75x.

Now calculate the cost for x = 5 using both expressions:

1) 11.75(5) + 5(5) = 58.75 + 25 = 83.75

2) 16.75(5) = 83.75

Of course you got the same result with both expressions.
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4 0
3 years ago
Sarah has a collection of nickels, dimes, and quarters worth $28.75. She has 10 more dimes than nickels and twice as many quarte
Ymorist [56]

Answer:

Step-by-step explanation:

Write an equation for each statement:

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"Sarah has a collection of nickels, dimes, and quarters worth $15.75."

.05n + .1d + .25q = 15.75

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"She has 10 more dimes than nickels"

d = n + 10

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"twice as many quarters as dimes."

q = 2d

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How many coins of each kind does she have?

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Take the 2nd equation and arrange it so n is in terms of d also

n + 10 = d

n = (d - 10)

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In the 1st equation substitute (d-10) for n and 2d for q:

.05n + .1d + .25q = 15.75

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.05(d-10) + .1d + .25(2d) = 15.75

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.05d - .5 + .1d + .5d = 15.75

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.65d - .5 = 15.75

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.65d = 15.75 + .5

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.65d = 16.25

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d = 16.25/.65

:

d = 25 dimes

:

Remember the statement "twice as many quarters as dimes."

q = 2(25)

q = 50 quarters

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The statement "She has 10 more dimes than nickels"

n = 25 - 10

n - 15 nickels

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Check our solutions

.05(15) + .1(25) + .25(50) =

.75 + 2.50 + 12.50 = 15.75 proves our solutions

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Rajan needs 1 liter of 15% hydrochloric acid solution for an experiment. He checks his storage cabinet, but he only has a 5-lite
Delvig [45]

Answer:

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  2. <em>0.25</em><em> liters of 45% hydrochloric acid solution.</em>

Step-by-step explanation:

Let us assume that, x liters of the 5% hydrochloric acid and y liters of the 45% hydrochloric acid solutions are combined.

As Rajan need total of 1 liter of solution, so

x+y=1

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As Rajan needs 5% hydrochloric acid and 45% hydrochloric acid to make a 1 liter batch of 15% hydrochloric acid, hence acid content of the mixture of two acids will be same as of the final one, so

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Putting value of x from equation 1 in equation 2,

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\Rightarrow 40y=15-5=10

\Rightarrow y=0.25

Putting the value of y in equation 1,

x=1-0.25=0.75

Therefore, Rajan must use 0.75 liters of 5% hydrochloric acid solution and 0.25 liters  of 45% hydrochloric acid solution.

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