Question

alis dog weighs 8 times as much as her cat. together, the two pets weigh 54 pynds. how much does Alis dog weigh?

Answer 1

The weight of the Alis dog is $\fbox{\bf48}$ pounds.

Further explanation:

Consider the weight of the Alis dog as $x$ pounds and weight of the cat as $y$ pounds.

Since, the weight of the Alis dog is 8 times the weight of the cat. It can be written as follows:

$x=8y$                                                                     ......(1)

Now, the total weight of the cat and dog are given as 54 pounds. It can be written as follows:

$x+y=54$                                                                 ......(2)

From equation (1), substitute $8y$ for $x$ in equation (2).

$\begin{aligned}8y+y&=54\\9y&=54\\y&=\dfrac{54}{9}\\y&=6\end{aligned}$

Thus, the weight of the cat is 6 pounds.

Substitute 6 for $y$ in equation (1) to obtain the weight of Alis dog as follows:

$\begin{aligned}x&=8(6)\\&=48\end{aligned}$

Thus, the weight of the Alis dog is 48 pounds.

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Answer Details :

Grade: Middle School .

Subject: Mathematics .

Chapter: linear equation.

Keywords:

lines, equation, pound, Alis dog, cat, weight, linear equation, zeros, x,y,x=8y,x+y=54, function, substitution, pets, direct substitution, elimination, graph, middle term factorization, fraction.