To solve the problem of how many kilograms of cement Shawn needs when he has 60 kilograms of sand, we can use the given ratio relationship between sand and cement.
The table describes the ratio of sand to cement as:
[tex]\[
\begin{array}{c|c}
\text{Number of Kilograms of Sand} & \text{Number of Kilograms of Cement} \\
\hline
3 & 4 \\
6 & 8 \\
9 & 12 \\
\end{array}
\][/tex]
From the table, we can see that this relationship is consistent. For every 3 kilograms of sand, 4 kilograms of cement are used.
To determine the amount of cement needed for 60 kilograms of sand, we need to maintain the same ratio. Let's denote the number of kilograms of cement needed as [tex]\( x \)[/tex].
The ratio of sand to cement is:
[tex]\[ \frac{3 \text{ kg of sand}}{4 \text{ kg of cement}} = \frac{60 \text{ kg of sand}}{x \text{ kg of cement}} \][/tex]
We can set up a proportion to solve for [tex]\( x \)[/tex]:
[tex]\[ \frac{3}{4} = \frac{60}{x} \][/tex]
To solve this proportion, we can use cross-multiplication:
[tex]\[ 3x = 4 \times 60 \][/tex]
Now, calculate the right-hand side:
[tex]\[ 3x = 240 \][/tex]
Next, solve for [tex]\( x \)[/tex] by dividing both sides by 3:
[tex]\[ x = \frac{240}{3} \][/tex]
[tex]\[ x = 80 \][/tex]
Therefore, Shawn should use 80 kilograms of cement for 60 kilograms of sand.
