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3 years ago

I need an equation that has variables on both sides were x = 17

Mathematics

1 answer:

Andrei [34K]3 years ago

5 0

3 (3 + x) = 5x - 25

9 + 3x = 5x - 25

Add 25 to each side

34 + 3x = 5x

Subtract 3x from each side

34 = 2x

Divide each side by 2

17 = x

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A cash box contains $74 made up of quarters, half-dollars, and one-dollar

Strike441 [17]

Answer:

25 one-dollar coins, 16 half-dollar coins, and 164 quarters

Step-by-step explanation:

First, set up equations based on the information given:

$0.25q+0.50h+1.00d=74$

$\displaystyle{h=\frac{3}{5}d+1}$

$q=4(d+h)$

Then, substitute q in the first equation with the expression from the third equation:

$0.25[4(d+h)]+0.50h+1.00d=74\\1d+1h+0.50h+1.00d=74\\2d+1.5h=74$

Next, substitute h in that equation with the expression from the second equation:

$\displaystyle{2d+1.5(\frac{3}{5}d+1)=74}$

$2d+0.9d+1.5=74\\2.9d+1.5=74$

Solve for d, the number of one-dollar coins:

$2.9d+1.5=74\\2.9d=72.5\\d=25$

Substitute 25 for d in the second equation to find h, the number of half-dollar coins:

$\displaystyle{h=\frac{3}{5}d+1}$

$\displaystyle{h=\frac{3}{5}(25)+1}$

$h=15+1\\h=16$

Substitute 25 for d and 16 for h in the third equation to find q, the number of quarters:

$q=4(d+h)\\q=4(25+16)\\q=4(41)\\q=164$

Then, verify that the coins total $74:

$0.25(164)+0.50(16)+1.00(25)=74\\41+8+25=74\\74=74\\\text{Check.}$

Next, verify that the number of half-dollar coins is one more than three-fifths of the number of one-dollar coins:

$\displaystyle{h=\frac{3}{5}d+1}$

$\displaystyle{16=\frac{3}{5}(25)+1}$

$16 = 15 + 1\\16 = 16\\\text{Check.}$

Finally, verify that the number of quarters is four times the number one-dollar and half-dollar coins together:

$q=4(d+h)\\164=4(25+16)\\164=4(41)\\164=164\\\text{Check.}$

6 0

3 years ago

What is the solution of 3x=67 ?

natta225 [31]

Answer:

22.3 repeating

Step-by-step explanation:

3x divided by 3x equals 1x or just x but to divide this you also have to divide the other side of the equals sign by 3 as well therefore the answer is 22.3 repeating

You might find it easy by putting it in fractions such as 3x/3x = 67/3 so x =22.3 repeating

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3 years ago

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Right angled triangle calc: find a, b=24, c=33.94113

Ksenya-84 [330]

Use the Pythagorean theorem...
a²+b²=c², in this case a²=c²-b²

a²+24²=33.94113²

a²+576=1,152.00031

a²=576.000306

a=24 (If you need the exact number, not rounded, it is 24.0000064)

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3 years ago

What is half of 90 ?

Anna35 [415]

half means 2

90 divided by 2

90/2

Answer: 45

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Which property is shown?

solniwko [45]

Associative Property of Addition hope this helps

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