Question

A recipe that uses 1/2 pound of almonds makes 5/6 cup of almond butter.

Which is a reasonable estimate for the amount of almond butter the recipe makes per pound of almonds?
a) less than 1 1/2 cup of almond butter
b) between 1 1/2 and 2 cups of almond butter
c) more than 2 cups of almond butter​

Answer 1

Answer: C

Explanation:

1/2 pound of almonds = 5/6 cup of almond butter

To find out how much almond butter 1 pound of almonds will make, we need to multiply both sides of the equation by 2:

1 pound of almonds = (2 × 1/2) pounds of almonds = 2 × 5/6 cups of almond butter

Simplifying, we get:

1 pound of almonds = 5/3 cups of almond butter

So, a reasonable estimate for the amount of almond butter the recipe makes per pound of almonds is more than 2 cups of almond butter. Therefore, the answer is (c) more than 2 cups of almond butter.

Answer 2

Answer: b) between 1 1/2 and 2 cups of almond butter

Explanation:

We can create a proportion to help us solve this question.

`\displaystyle ((1)/(2) lbs\;almonds)/((5)/(6)lbs\;butter ) =(1lbs\;almonds)/(xlbs\;butter)`

Now we can cross multiply.

`\displaystyle (1)/(2) *x=(5)/(6) *1`

`\displaystyle (1)/(2)x =(5)/(6)`

Next, we will divide both sides of the equation by one-half.

`\displaystyle x =(5)/(6)/ (1)/(2)`

`\displaystyle x =(5)/(6)* (2)/(1)`

`\displaystyle x =(10)/(6)`

Lastly, we will find which answer option this falls under by creating an improper fraction. This leads us to answer optoin b, b) between 1 1/2 and 2 cups of almond butter.

`\displaystyle 10-6=4\text{, so } 1(4)/(6) =1(2)/(3)`