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3 years ago

What value of "p" makes the equation true ?

Mathematics

2 answers:

Westkost [7]3 years ago

6 0

32 * 125 = (32 * 100) + (32 * p)
4000 - 4000 = 3200 + 32p - 4000
32p - 0 = 3200 + 32p + 32p - 4000 -32p
-32p = 3200 - 4000
-32 / -32p = -800 / -32
p = 25

Hoochie [10]3 years ago

3 0

32 × 125 = (32 × 100) + (32 × p)

32 × (100 + 25) = (32 × 100) + (32 × p)

(32 × 100) + (32 × 25) = (32 × 100) + (32 × p)

(32 × 25) = (32 × p)

p = 25

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Two mechanics worked on a car. The first mechanic worked for 10 hours, and the second mechanic worked for 15 hours together they

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Answer:

Step-by-step explanation:

We need a system of equations here, 2 equations for 2 unknowns. The unknowns will be x and y and will represent the rates of 2 mechanics. The first equation will relate the 2 mechanics' rates and the second will involve the total they charged at their respective rates having worked a specific number of hours on the car.

We are told that the 2 rates added together was 170 per hour, so the first equation will be

x + y = 170

The next equation will be the rates times the number of hours worked:

10x + 15y = 2175 This means that the mechanic charging x dollars per hour worked on the car for 10 hours, and the mechanic charging y dollare per hour worked on the car for 15 hours, and that the amount this added up to was 2175.

We solve the first equation for y, just because. You could also solve it for x, if you want. Doesn't matter; you'll get the same answer either way.

y = 170 - x and sub that for y in the the second equation. Then we will have an equation with only 1 unknown in it:

10x + 15(170 - x) = 2175 and

10x + 2550 - 15x = 2175 and

-5x = -375 so

x = 75. One mechanic, the one who worked for 10 hours on te car, charges 75 per hour. To find out how much the other guycharges, go back to the first equation and sub in 75 for x:

75 + y = 170 so

y = 95 per hour.

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3 years ago

If 4 students share 30 ft.² wall equally how many square feet of the wall will be painted by each student

Brut [27]

Answer:

7.5 ft²/student

Step-by-step explanation:

This is a "unit rate" problem.

30 ft²

------------------ = 7.5 ft²/student

4 students

Each student will paint 7.5 ft² of the wall.

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3 years ago

Read 2 more answers

A 15-ft by 15-ft rectangular swimming pool is surrounded by a walkway of uniform width. If the total area of the walkway is 13

andrezito [222]

Answer:

2ft wide

Step-by-step explanation:

Total Area = Area of the summing pool + total Area of the walkway.

Area of the summing pool = 15 × 15 = 225ft²

And total area of walkway = 136ft²

∴ total area = 225 + 136 = 361 ft².

Let w = The width of the walkway.

Since the walkway has a uniform width

∴ Total Area of pool and walkway = (15+2w)(15+2w)

⇒ (15+2w)(15+2w) = 361........................(1)

Expanding Equation(1)

15×15 + 15×2w + 2w×15 + 2w×2w = 361

⇒ 225 + 30w + 30w + 4w² = 361................(2)

Rearranging equation(2) above and collecting like terms

4w²+60w = 361-225

4w² + 60w = 136..............................(3)

Dividing all through equation(3) by 4

4w²/4 + 60w/4 = 136/4

w² + 15w = 34..............(4)

rearranging equation(4)

w²+15w -34 = 0

Using factorization method to solve the quadratic equation,

w² + 15w - 34 = 0

Two numbers whose sum give +15 and whose product gives -34

are +17 and -2.

∴ w² -2w +17w -34 =0

grouping the equation,

(w²-2w) + (17w-34) =0

Bringing out the common terms in both bracket.

w(w-2) +17(w-2) =0

since both term in the bracket are the same, take one of the term in the bracket and form a bracket for the outer term i.e

(w-2)(w+17)=0.

Either w-2 =0

w=+2

OR w+17 =0

w=-17.

The right answer is w=+2 as wide can not be negative.

∴ The walkway is 2ft wide.

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