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3 years ago

A student wrote the equation 4(x+5.5)=3(1.5x+4.75) to represent the problem shown. Find her mistake and correct it.

Mathematics

1 answer:

Afina-wow [57]3 years ago

8 0

Answer:

$8.5

Step-by-step explanation:

The first group consists of Petra and 4 friends, so the total number of members is 5, therefore the left side of equation should be:

5(x + 5.5)

The second group consists of 4 people, Valentina and 3 friends, therefore the right side of the equation should be:

4(1.5x + 4.75)

Solving the equation to find the cost of a ticket for Petra's group:

5(x + 5.5) = 4(1.5x + 4.75)
5x + 27.5 = 6x + 19
6x - 6x = 27.5 - 19
x = 8.5

Cost of a ticket is $8.5

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The answer for the first question is:

12/80 =

12 ÷ 80 =

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(0.15 × 100)% =

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Roman55 [17]

Answer:

$(x,y)=\left(\; \boxed{-1,-8} \; \right)\quad \textsf{(smaller $x$-value)}$

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Step-by-step explanation:

Given system of equations:

$\begin{cases}y=x^2-9\\y=4x-4\end{cases}$

To solve by the method of substitution, substitute the first equation into the second equation and rearrange so that the equation equals zero:

$\begin{aligned}x^2-9&=4x-4\\x^2-4x-9&=-4\\x^2-4x-5&=0\end{aligned}$

Factor the quadratic:

$\begin{aligned}x^2-4x-5&=0\\x^2-5x+x-5&=0\\x(x-5)+1(x-5)&=0\\(x+1)(x-5)&=0\end{aligned}$

Apply the zero-product property and solve for x:

$\implies x+1=0 \implies x=-1$

$\implies x-5=0 \implies x=5$

Substitute the found values of x into the second equation and solve for y:

$\begin{aligned}x=-1 \implies y&=4(-1)-4\\y&=-4-4\\y&=-8\end{aligned}$

$\begin{aligned}x=5 \implies y&=4(5)-4\\y&=20-4\\y&=16\end{aligned}$

Therefore, the solutions are:

$(x,y)=\left(\; \boxed{-1,-8} \; \right)\quad \textsf{(smaller $x$-value)}$

$(x,y)=\left(\; \boxed{5,16} \; \right)\quad \textsf{(larger $x$-value)}$

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Answer:

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