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g100num [7]
3 years ago
7

Luke buys 4 bolts and 6 washers for $2.20 and Holly spends $1.80 on 3 bolts and 5 washers at the same local hardware store. Dete

rmine the costs of a bolt and a washer.
Mathematics
1 answer:
blondinia [14]3 years ago
8 0

Answer:

Cost of bolts = x = $0.3

Cost of washers = y = $0.167

Step-by-step explanation:

Let us represent:

Cost of bolts = x

Cost of washers = y

Luke buys 4 bolts and 6 washers for $2.20

Hence:

4x + 6y = 2.20....Equation 1

Holly spends $1.80 on 3 bolts and 5 washers at the same local hardware store.

3x + 5y = 1.80....Equation 2

Combining both Equations

4x + 6y = 2.20....Equation 1

3x + 5y = 1.80....Equation 2

Multiply Equation 1 by 3 and Equation 2 by 4 to eliminate x

12x + 18x = 6.6.....Equation 4

12x + 20x = 7.2.......Equation 5

Substract Equation 4 from 5

= 2x = 0.6

x = 0.6/2

x = $0.3

Solving for y

4x + 6y = 2.20....Equation 1

4 × 0.3 + 6y = 2.2

1.2 + 6y = 2.2

6y = 2.2 - 1.2

6y = 1.0

y = 1.0/6

y = $0.167

Cost of bolts = x = $0.3

Cost of washers = y = $0.167

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Mel used partial quotients to find the quotient of 378 divided by 3.What could be the partial quotient that Mel found?
Genrish500 [490]

Answer:

The partial quotients are 100, 20 and 6. The quotient is 126.

Step-by-step explanation:

The dividend is 378 and the divisor is 3.

First find the factors of 3, near to 300.

3\times 1=3

3\times 10=30

3\times 100=300

The value 300 is less than 378, so record the partial quotient 100 and subtract 300 from 378. Repeat the same process until the dividend has been zero.

Now the remaining divide is 78.

First find the factors of 3, near to 78.

3\times 20=60

3\times 30=90

Since 90>78, therefore 30 is not a partial quotient. The value 60 is less than 78 , so record the partial quotient 20 and subtract 60 from 78.

Now the remaining divide is 18.

3\times 6=18

The number 6 is a partial quotient.

Therefore  partial quotients are 100, 20 and 6. Add the partial quotient to find quotient.

100+20+6=126

3 0
3 years ago
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san4es73 [151]

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5 0
2 years ago
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Flying against the wind, an airplane travels 7520 kilometers in 8 hours. Flying with the wind, the same plane travels 6500 kilom
bezimeni [28]

Answer:

Rate of plane in still air = 1120 km/h

Rate of wind = 180 km/h

Step-by-step explanation:

Let the rate (speed) of the plane in still air = u km/h

Let the rate (speed) of the wind = v km/h

Formula for speed is:

Speed = \dfrac{Distance}{Time}

Given that against the wind, airplane travels 7520 km in 8 hours.

The speed against the wind will be slower so,

Against the wind, speed = (u -v ) km/h

Using above formula:

(u-v) = \dfrac{7520}{8} km/h\\(u-v) = 940 km/h ..... (1)

Given that with the wind, airplane travels 6500 km in 5 hours.

The speed with the wind will be faster so,

With the wind, speed = (u +v ) km/h

Using above formula:

(u+v) = \dfrac{6520}{5} km/h\\(u+v) = 1300 km/h ..... (2)

Adding (1) and (2) to solve for u and v:

2u = 2240\\\Rightarrow u = 1120\ km/h

Putting u in (1):

1120-u=940\\\Rightarrow u = 180\ km/h

So, the answers are:

<em>Rate of plane in still air = 1120 km/h</em>

<em>Rate of wind = 180 km/h</em>

<em></em>

6 0
3 years ago
What can be used to show the difference in variation for two populations that have equivalent measures of center?.
MakcuM [25]
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7 0
3 years ago
Find the slope of the line,<br> HELPPPP
nlexa [21]

Answer:

Slope: 2

Step-by-step explanation:

The slope of a line is when x increases by an amount, y increases by an amount. We can find the slope of a linear graph by taking 2 points. I will use (0,3) and (-1,1)

We see that the y-values are 4 from each other, and that the x-values are 2 from each other.

Now, we can use a method called rise over run, which is y-value/x-value.

\frac{4}{2} =2

Therefore, the slope is 2.

7 0
2 years ago
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