Respuesta :
The number of small boxes purchased is 4.
The number of large boxes purchased is 2.
The number of nails in a small box is 50, and the number of nails in a large box is 450.
The total number of nails bought is 1100.
Let the number of large boxes be "x".
The number of small boxes is "2x".
An equation is a formula in mathematics that expresses the equivalence of two expressions by linking them with the equal sign.
The equation can be formed as given below :
x*450 + 2x*50 = 1100
450x + 100x = 1100
550x = 1100
x = 2
The number of small boxes purchased is 2*x = 2*2 = 4.
The number of large boxes purchased is x = 2.
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Answer:
4 boxes of small nails.
2 boxes of large nails.
Step-by-step explanation:
Define the variables:
- Let x = the number of small boxes of nails.
- Let y = the number of large boxes of nails.
Given information:
- Small box = 50 nails.
- Large box = 450 nails.
- The contractor bought twice as many small boxes as large boxes.
- Total number of nails bought = 1100 nails.
Create a system of equations with the given information and defined variables:
[tex]\begin{cases}x=2y\\50x+450y=1100\end{cases}[/tex]
Substitute the first equation into the second equation and solve for y:
[tex]\implies 50(2y)+450y=1100[/tex]
[tex]\implies 100y+450y=1100[/tex]
[tex]\implies 550y=1100[/tex]
[tex]\implies \dfrac{550y}{550}=\dfrac{1100}{550}[/tex]
[tex]\implies y=2[/tex]
Substitute the found value of y into the first equation and solve for x:
[tex]\implies x=2(2)[/tex]
[tex]\implies x=4[/tex]
Therefore the contractor purchased:
- 4 boxes of small nails.
- 2 boxes of large nails.
