+2442 2 cups of sugar
1/3 cups of butter
Setup proportions to solve for both the sugar and butter. In a recipe, all ingredients must be proportional because otherwise, the meal will be not be exactly as the recipe calls for:
Let x = the cups of sugar
Let y = the cups of butter
\(\frac{\frac{3}{4}}{x}=\frac{\frac{3}{8}}{1}=\frac{\frac{1}{8}}{y}\)
We should solve each proportional individually. I'll solve for the cups of sugar first:
| \(\frac{\frac{3}{4}}{x}=\frac{\frac{3}{8}}{1}\) | Solve by cross multiplying |
| \(\frac{3}{4}=\frac{3}{8}x\) | Multiply by 8/3 on both sides to isolate x |
| \(x=\frac{3}{4}*\frac{8}{3}\) | Simplify the right hand side |
| \(x=\frac{24}{12}=2\)cups of sugar! | I multiplied the fraction and then reduced it to simplest terms. |
Let's utilize the exact same process for solving for y, the amount of cups of butter:
| \(\frac{\frac{3}{8}}{1}=\frac{\frac{1}{8}}{y}\) | Cross muliply and solve for y |
| \(\frac{3}{8}y=\frac{1}{8}\) | Multiply by 8/3 on both sides |
| \(y=\frac{1}{8}*\frac{8}{3}\) | Simplify the right hand side |
| \(y=\frac{8}{24}=\frac{1}{3}\) cups of butter! | I multiplied the fraction and reduced it to simplest terms. |
+2442 \(y=-12\)
| \(5(y+2)=2(2y-1)\) | This is the given equation. First, distribute the 5 and 2 |
| \(5y+10=4y-2\) | Subtract 4y on both sides |
| \(y+10=-2\) | Subtract 10 on both sides |
| \(y=-12\) | We found y, so we are done! |
If you are ever unsure whether or not your answer is correct, plug the y-value into the equation. Then, check to see that the equation is true:
| \(5(-12+2)=2(2(-12)-1)\) | Check to see if this is true by simplifying. Let's clean this up |
| \(5*-10=2(-24-1)\) | |
| \(5*-10=2*-25\) | |
| \(-50=-50\) | This is true, so the answer, y=-12 is the correct and only correct solution |
+2442 \(\frac{2.5}{2}=1.25\)
One half of 2.5 is the equivalent of saying what is 1/2 * 2.5. "Of" is referring to multiplication, in this case:
| \(\frac{1}{2}*\frac{2.5}{1}\) | Multiply the fractions together and then you are done! Remember, when multiplying fractions, simply multiply the numerator and denominator. |
| \(\frac{2.5}{2}=1\frac{1}{4}=1.25\) | |
