The question wants us to use less icing sugar and chocolate chips to make smaller cookies with less sugar. For example, if we made
a half recipe, but made \(12\) smaller cookies, each cookie would have \(14.25 \;[g]\) of sugar. Let's set up an equation to represent the total amount of sugar in the mixure:
\(20 \cdot 12 = 98 \cdot x + 8 \cdot y\)
We want the total amount of sugar to be \(20\;[g]\) times \(12\) cookies. This equation has two unknowns. We need another equation. In the originial recipe, the number of servings of
chocolate chips is twice as much as the number of servings of icing sugar. We should keep this ratio so the cookies aren't gross (just a little healither!). This can be written as:
\(y = 2 \cdot x\)
Now we have two equations with two unknowns. Use substitution to solve:
\(20 \cdot 12 = 98 \cdot x + 8 \cdot y\)
\(240 = 98 \cdot x + 8 \cdot y\)
\(240 = 98 \cdot x + 8 \cdot (2 \cdot x)\)
\(240 = 98 \cdot x + 16 \cdot x\)
\(240 = 114 \cdot x\)
\(x = \frac{240}{114}\)
\(x \approx 2.1\)
Now plug back in to solve for \(y\):
\(y = 2 \cdot x\)
\(y = 2 \cdot 2.1\)
\(y \approx 4.2\)
Therefore, we should use \(2\) servings of icing sugar and \(4\) servings of chocolate chips . We should make about a \(\frac{2}{3}\) recipe and make smaller cookies.