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zzz [600]
3 years ago
5

3. At a bargain store, Tanya bought 4 items that each cost the same amount. Tony bought 5 items that each cost the same amount,

but each was $1.25 less than the items that Tanya bought. Both Tanya and Tony paid the same amount of money. What was the individual cost of each person's items? (a) Write an equation. Let x represent the cost of one of Tanya's items. (b) Solve the equation. Show your work. (c) Check your solution. Show your work. (d) State the solution in complete sentences
Mathematics
1 answer:
FinnZ [79.3K]3 years ago
6 0

We'll do it in cents and convert when we have to.

Tanya paid x per item, a total of 4x.

Tony paid x-125 per item (in cents) for a total of 5(x-125)

4x = 5(x-125)

4x = 5x - 625

x = 625 = $6.25  

Check:

4(625) = 2500

5(625-125)=2500, same, checks

Answer: Tanya paid $6.25 per item, Tony $5.00 per item


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For a certain bathtub, the hot water faucet can fill the tub in 12 minutes. The cold water faucet can fill the tub in 8 minutes.
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If both faucets are used together, it time taken by them to fill the tub is 4.8 minutes.

<h3>What is the concept of time and work?</h3>

Time and work share a fundamental idea in common with other arithmetic topics, namely the idea of proportionality.

When the amount of work is constant, efficiency is inversely proportional to the length of time required.

Important Time and Work Formula:

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Calculation for the time taken by both faucet to fill the tub.

The unit should be tub per minute.

Then, do the reciprocal of the result to have minute per tub.

The hot water faucet can fill the tub in 12 minutes.

The cold water faucet can fill the tub in 8 minutes.

The filling rate for both faucets filling the tub at the same time is the sum of their rates.

Let 't' be the time taken by both faucets.

Then,

\frac{1}{12} +\frac{1}{8} =\frac{1}{t}

\frac{8+12}{8*12} =\frac{1}{t}

\frac{1}{t} =\frac{20}{96}

\frac{t}{1} =\frac{96}{20}

t = 4.8

Therefore, the time taken by both faucets to fill the tub is 4.8 minutes.

To know more about the formula for calculating power, here

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