Answered

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An artist bought a set of 10 paintbrushes that contained [tex]\(x\)[/tex] small paintbrushes and [tex]\(y\)[/tex] large paintbrushes. The number of small paintbrushes in the set was 4 times the number of large paintbrushes in the set.

Which system of equations can be used to find the numbers of small paintbrushes and large paintbrushes in the set?

(A)
[tex]\[ \begin{array}{l}
x + y = 10 \\
x = 4y
\end{array} \][/tex]

(B)
[tex]\[ \begin{array}{l}
x - y = 10 \\
x = 4y
\end{array} \][/tex]

(C)
[tex]\[ \begin{array}{l}
x + y = 10 \\
y = 4x
\end{array} \][/tex]

(D)
[tex]\[ \begin{array}{l}
x - y = 10 \\
y = 4x
\end{array} \][/tex]

Sagot :

GinnyAnsweridn
To determine the correct system of equations for the given problem, let's analyze the information provided:

1. The artist bought [tex]$x$[/tex] small paintbrushes and [tex]$y$[/tex] large paintbrushes.
2. The total number of paintbrushes is 10.
3. The number of small paintbrushes is 4 times the number of large paintbrushes.

We need to translate this information into mathematical equations.

First, the total number of paintbrushes:
[tex]\[ x + y = 10 \][/tex]

This equation indicates that the sum of small paintbrushes [tex]\(x\)[/tex] and large paintbrushes [tex]\(y\)[/tex] is 10.

Next, the relationship between the number of small and large paintbrushes:
[tex]\[ x = 4y \][/tex]

This equation tells us that the number of small paintbrushes [tex]\(x\)[/tex] is 4 times the number of large paintbrushes [tex]\(y\)[/tex].

Now, we have a system of equations:
[tex]\[ \begin{aligned} x + y &= 10 \\ x &= 4y \end{aligned} \][/tex]

Thus, the system of equations that can be used to find the numbers of small paintbrushes and large paintbrushes in the set is:

(A)
[tex]\[ \begin{array}{l} x + y = 10 \\ x = 4 y \end{array} \][/tex]

So, the correct choice is (A).
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