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steposvetlana [31]
2 years ago
12

The length of a rectangle is 4 m more than the width. If the area of the rectangle is 77 m2. How many meters long is the width o

f the rectangle?
Mathematics
1 answer:
kenny6666 [7]2 years ago
7 0

Step-by-step explanation:

length = width + 4

length×width = 77

using the first in the second equation

(width + 4)×width = 77

width² + 4width = 77

now, what square or squaring factors can create this ?

we are looking for (width + a)(width + b).

we know, this is

width² + (a+b)width + ab

so, what a, b can create 4 (the factor in our actual equation) ?

1, 3 and 2, 2, if we are only looking at whole numbers.

and which of the possibilities can we use to turn 77 into a square number ?

81 is only 4 away ...

2+2 = 4.

aha !

so, we can actually say our equation is

width² + 4width + 4 = 77 + 4

and then

(width + 2)² = 81

width + 2 = 9

width = 7 m

length = width + 4 = 7 + 4 = 11 m

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A ride at a carnival has two types of cars for children to ride one type has two seats and one has four seats there are 25 cars
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Answer:

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Step-by-step explanation:

To solve this problem you need to create a system of equations. In these equations, use a = 2-seated car and b = 4- seated car

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The next equation you can make is 2a + 4b = 70 because the number of seats provided by the 2-seated cars plus the number of seats provided by the 4-seated cars will equal 70 total seats.

Next, line up the equations and solve:

Step one: Line up the equations

                a +  b = 25

             2a + 4b = 70

Step two: Multiply the top equation by -2 so that you can add both of                                        the equations together

             -2(a) + -2(b) = 25(-2)   ⇒   -2a - 2b = -50

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Step three: Add the equations

               -2a - 2b = -50

              + 2a + 4b = 70

            ______________

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Step four: Divide both sides by 2 in order to solve for b

                2b = 20 ⇒ b = 10  

Because b represents the number of 4-seated cars, you now know that there are 10 4-seated cars on the ride.          

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