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Veseljchak [2.6K]
2 years ago
5

Kim and Danielle each improved their yards by planting hostas and ivy. They bought their supplies from the same store. Kim spent

$62 on 5 hostas and 4 pots of ivy. Danielle spent $144 on 8 hostas and 12 pots of ivy. What is the cost of one hosta?
Mathematics
1 answer:
svetlana [45]2 years ago
8 0

Answer:

The cost of one hosta is $6

Step-by-step explanation:

A system of linear equations is a set of two or more equations of the first degree, in which two or more unknowns are related.

Solving a system of equations consists of finding the value of each unknown so that all the equations of the system are satisfied.

In this case, the variables are:

  • x = price of a hosta .
  • y = price of a pot of ivy.

If Kim spent $62 on 5 hostas and 4 pots of ivy, t his is represented by the equation: 5*x +4*y= 62

If Danielle spent $144 on 8 hostas and 12 pots of ivy, t his is represented by the equation: 8*x +12*y=144

So, the system of equations to solve is:

\left \{ {{5*x+4*y=62} \atop {8*x+12*y=144}} \right.

One way to solve a system of equations is through the substitution method, which consists of solving or isolating one of the unknowns (for example, x) and substituting its expression in the other equation. In this way, you obtain an equation of the first degree with the other unknown, and. Once solved, you calculate the value of x by substituting the already known value of y.

Isolating y from the first equation:

y=\frac{62-5*x}{4}

and replacing this expression in the second equation you get:

8*x +12*\frac{62-5*x}{4}=144

Solving:

8*x +\frac{12}{4}*(62-5*x)=144

8*x + 3*(62-5*x)=144

8*x + 3*62 - 3*5*x=144

8*x + 186 - 15*x=144

8*x  - 15*x=144 -186

(-7)*x= -42

x= (-42)÷ (-7)

x= 6

<u><em>The cost of one hosta is $6</em></u>

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andrezito [222]

Answer:

l=31\ cm\\\\w=24\ cm

Step-by-step explanation:

The formula that is used to calculate the area of a rectangle is:

A=lw

Where "l" is the lenght and "w" is the width.

You know that the area of that rectangle is:

A=744\ cm^2

And, according to the exercise, its lenght is 7 more than its width; then:

l=w+7

Then, you can make the corresponding substitution into the formula A=lw:

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Simplify:

744=w^2+7w\\\\w^2+7w-744=0

Factor the equation. Find two numbers whose sum is 7 and whose product is -744. These are 31 and -24.

Then, you get:

(w-24)(w+31)=0\\\\w_1=24\\\\w_2=-31

The width of the rectangle is the positive value:

w=24\ cm

Then, the lenght is:

l=24+7\\\\l=31\ cm

8 0
3 years ago
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Answer:

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Step-by-step explanation:

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One quarter of 120 is 30, so - 30 would give discounted price of $90.

Similarly you could think of it like the discounted price is 75% of the original one and do 120x0.75=90 to find 75% of 120.

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Answer:

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Step-by-step explanation:

Given equation is:

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