Question

Steve is planning to bake 3 loaves of bread. Each loaf calls for $5\dfrac{1}{4}$ cups of flour. He knows he has 20 cups on hand. Will he have enough flour left for a cake recipe that requires $3\dfrac{3}{4}$ cups?

Answer 1

Hint: We start solving the problem by finding the total number of cups required to bake 3 loaves of bread using the information about the number of cups required to bake 1 loaf of bread. We then find the remaining cups of flour by subtracting the cups of flour used to bake 3 loaves of bread from 20 cups of flour. We then check the obtained value of remaining cups with the requirement of cups to make a cake recipe.

Complete step-by-step answer:
According to the problem, we have given Steve is planning to bake 3 loaves of bread and each loaf requires $5\dfrac{1}{4}$ cups of flour. Steve has 20 cups on hand and we need to find whether he has enough flour left for a cake recipe that requires $3\dfrac{3}{4}$ cups.
Let us find the total no. of cups of flour required to bake 3 loaves of bread.
We need to multiply $5\dfrac{1}{4}$ cups with 3 in order to get 3 loaves of bread.
So, total flour required for 3 loaves of bread is $3\times \left( 5\dfrac{1}{4} \right)$.
$\Rightarrow 3\times \left( 5+\dfrac{1}{4} \right)$.
$\Rightarrow 3\times \left( \dfrac{20+1}{4} \right)$.
$\Rightarrow 3\times \left( \dfrac{21}{4} \right)$.
$\Rightarrow \dfrac{63}{4}$.
So, we require $\dfrac{63}{4}$ cups of flour to bake 3 loaves of bread.
We subtract $\dfrac{63}{4}$ cups from 20 cups to get the remaining cups of flour.
Remaining cups of flour = $20-\dfrac{63}{4}$.
$\Rightarrow \dfrac{80-63}{4}$.
$\Rightarrow \dfrac{17}{4}$.
$\Rightarrow \dfrac{16+1}{4}$.
$\Rightarrow 4+\dfrac{1}{4}$.
$\Rightarrow 4\dfrac{1}{4}$ cups of flour.
We have found that there is $4\dfrac{1}{4}$ cups of flour remaining which is greater than the $3\dfrac{3}{4}$ cups of flour.
So, Steve has enough flour left to make a cake recipe with $3\dfrac{3}{4}$ cups of flour.

Note: Whenever, we get a mixed fraction in the problem, we should convert them into the full fractions to do the problems. We can also check by converting all into fractions instead of the mixed fractions as checking the values of numerator with common denominator is easier to compare. Similarly, we can expect problems to find the total number of cups used up for one or more cake recipes.