Question $4$:

$(20$ Points$)$

You are provided with the gradation data for three aggregate sources as shown in the table below:

$\backslash$begin$\{$tabular$\}\{$cccc$\}$

$\backslash$begin$\{$tabular$\}\{$c$\}$

Sieve Size $\backslash \backslash$

$($mm$)$

$\backslash$end$\{$tabular$\}$ & $\backslash$begin$\{$tabular$\}\{$c$\}$

Aggregate Source A $(\backslash \%\backslash \backslash$

Passing$)$

$\backslash$end$\{$tabular$\}$ & $\backslash$begin$\{$tabular$\}\{$c$\}$

Aggregate Source B $(\backslash \%\backslash \backslash$

Passing$)$

$\backslash$end$\{$tabular$\}$ & $\backslash$begin$\{$tabular$\}\{$c$\}$

Aggregate Source C $(\backslash \%\backslash \backslash$

Passing$)$

$\backslash$end$\{$tabular$\}\backslash \backslash$

$19\mathrm{.}0$ & $100$ & $100$ & $100\backslash \backslash$

$12\mathrm{.}5$ & $95$ & $85$ & $92\backslash \backslash$

$9\mathrm{.}5$ & $80$ & $75$ & $88\backslash \backslash$

$4\mathrm{.}75$ & $65$ & $50$ & $60\backslash \backslash$

$2\mathrm{.}36$ & $55$ & $40$ & $45\backslash \backslash$

$1\mathrm{.}18$ & $45$ & $30$ & $35\backslash \backslash$

$0\mathrm{.}600$ & $30$ & $20$ & $25\backslash \backslash$

$0\mathrm{.}300$ & $18$ & $12$ & $15\backslash \backslash$

$0\mathrm{.}150$ & $12$ & $8$ & $10\backslash \backslash$

$0\mathrm{.}075$ & $5$ & $5$ & $5$

$\backslash$end$\{$tabular$\}$

Using the provided aggregate gradations, calculate the percentage of each aggregate source $($A$,$ B $,$ and C $)$ required in the blend to meet the Superpave aggregate gradation specification for a $12\mathrm{.}5$ mm Nominal Maximum Aggregate Size $($NMAS$).$

Ensure that the combined blend meets the Superpave gradation requirements for each sieve size within the specified limits$.$ Show your calculations.