To determine the initial amount of ice cream Ms. Leong had, we need to work backwards from the amount left after sales.
1. Chocolate Ice Cream:
- Ms. Leong sold [tex]\(\frac{3}{4}\)[/tex] of her chocolate ice cream.
- After selling, she had 20 scoops left.
Let's denote the initial amount of chocolate ice cream as [tex]\(C\)[/tex]. Since she sold [tex]\(\frac{3}{4}\)[/tex] of it, the remaining [tex]\(\frac{1}{4}\)[/tex] is what she has left.
Therefore, we can write the equation:
[tex]\[
\frac{1}{4}C = 20
\][/tex]
Solving for [tex]\(C\)[/tex], we multiply both sides by 4:
[tex]\[
C = 4 \times 20 = 80
\][/tex]
So, initially, she had 80 scoops of chocolate ice cream.
2. Vanilla Ice Cream:
- Ms. Leong sold [tex]\(\frac{1}{2}\)[/tex] of her vanilla ice cream.
- After selling, she had 30 scoops left.
Let's denote the initial amount of vanilla ice cream as [tex]\(V\)[/tex]. Since she sold [tex]\(\frac{1}{2}\)[/tex] of it, the remaining [tex]\(\frac{1}{2}\)[/tex] is what she has left.
Therefore, we can write the equation:
[tex]\[
\frac{1}{2}V = 30
\][/tex]
Solving for [tex]\(V\)[/tex], we multiply both sides by 2:
[tex]\[
V = 2 \times 30 = 60
\][/tex]
So, initially, she had 60 scoops of vanilla ice cream.
3. Total Initial Amount of Ice Cream:
- Now, we just add the initial amounts of chocolate and vanilla ice cream to find the total.
[tex]\[
\text{Total} = C + V = 80 + 60 = 140
\][/tex]
Therefore, Ms. Leong initially had 140 scoops of ice cream.
