Question

helena needs 3.5 cups of flour per loaf of bread and 2.5 cups of flour per batch of muffins. she also needs 0.75 cup of sugar per loaf of bread and 0.75 cup of sugar per batch of muffins. helena has 17 cups of flour and 4.5 cups of sugar available for baking.

Answer 1

Let $x$ be the number of loaves of bread that Helena can bake, and let $y$ be the number of batches muffins she can bake.

We know from our problem that she needs 3.5 cups of flour per loaf of bread and 2.5 cups of flour per batch of muffins. Since $x$ is the number of loaves of bread and $y$ is the number of muffins, we can express this as $3.5x+2.5y$. We also now that she has 17 cups of flour, so the cups of flour in the breads and muffins must be equal to 17; in other words: $3.5x+2.5y$ This is going to be equation (1)

We also know from our problem that she needs 0.75 cup of sugar per loaf of bread and 0.75 cup of sugar per batch of muffins. Since $x$ is the number of loaves of bread and $y$ is the number of batches of muffins, we can express this as $0.75x+0.75y$. We also know that she has a total of 4.5 cups of sugar available for baking, so the total sugar in brads and muffins must be 4.5 cups; in other words: $0.75x+0.75y=4.5$ This is going to be equation (2)

We created a system of equations with the information in our problem, so let's solve the system to find how much of each she can bake.

$\left \{ {{3.5x+2.5y=17} equation(1)\atop {0.75x+0.75y=4.5}equation(2)} \right.$

Step 1. Solve for $x$ in equation (2)

$0.75x+0.75y=4.5$

$0.75x=4.5-0.75y [/tex[tex] x=\frac{4.5-0.75y}{0.75}$

$x=\frac{4.5}{0.75} -\frac{0.75y}{0.75}$

$x=6-y$ equation (3)

Step 2. Replace equation (3) in equation (1) and solve for $y$

$3.5x+2.5y=17$

$3.5(6-y)+2.5y=17$

$21-3.5y+2.5y=17$

$21-y=17$

$-y=-4$

$y=4$ equation (4)

Step 3. Replace equation (4) in equation (3)

$x=6-y$

$x=6-4$

$x=2$

We can conclude that Helena can bake 2 loaves of bread and 4 batches of muffins with 17 cups of four and 4.5 cups of sugar.

Answer 2

The correct answer is:

She can make 2 loaves of bread and 4 batches of muffins.

Explanation:

Let b represent bread and m represent muffins.

The equation for the amount of flour she needs is 3.5b+2.5m=17.

The equation for the amount of sugar she needs is 0.75b+0.75m=4.5.

To solve this, we will want to eliminate one of the variables. To do this, we will make the coefficients of one of the variables the same. If we multiply 2.5 by 0.3, we get 0.75; this is what we will do to the first equation:

$\left \{ {{0.3(3.5b+2.5m=17)} \atop {0.75b+0.75m=4.5}} \right. \\ \\\left \{ {{1.05b+0.75m=17} \atop {-(0.75b+0.75m=4.5)}} \right. \\ \\0.3b=0.6 \\ \\\frac{0.3b}{0.3}=\frac{0.6}{0.3} \\ \\b=2$

She can bake two loaves of bread.

Substituting 2 for b in the first equation, we have

3.5(2)+2.5m=17

7+2.5m=17

Subtract 7 from each side:

7+2.5m-7=17-7

2.5m=10

Divide both sides by 2.5:

2.5m/2.5 = 10/2.5

m = 4

She can bake 4 batches of muffins.