Tuesday Math Problem $\newline$ There are some apples and $8$ pears in a basket, each of them green or yellow. There are three more apples than the total number of green fruits. There are $6$ yellow pears. How many yellow apples are there in the basket? $\newline$ Show your work.

Full solution

Q. Tuesday Math Problem

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There are some apples and

8

pears in a basket, each of them green or yellow. There are three more apples than the total number of green fruits. There are

6

yellow pears. How many yellow apples are there in the basket?

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Show your work.

Denote Fruits Count Variables: Let's denote the total number of green fruits as $G$ , the number of apples as $A$ , and the number of yellow apples as $Y_{\text{apples}}$ . According to the problem, there are $8$ pears in total, and $6$ of these are yellow. This means there are $8 - 6 = 2$ green pears. Since the pears are either green or yellow, there are no yellow pears to consider beyond the $6$ already counted.
Calculate Green Pears: Now, we know that there are $3$ more apples than the total number of green fruits. This can be expressed as $A = G + 3$ .
Determine Apple Relationship: Since we have $2$ green pears and the rest of the green fruits are apples, we can say that the number of green apples is $G - 2$ . We also know that the total number of apples is the sum of green apples and yellow apples, so $A = (G - 2) + Y_{\text{apples}}$ .
Solve for Yellow Apples: Substituting the expression for $A$ from the second step into the equation from the third step, we get $G + 3 = (G - 2) + Y_{\text{apples}}$ . Simplifying this, we can solve for the number of yellow apples: $Y_{\text{apples}} = 3 + 2 = 5$ .