Answer :
Sure, let's go through the solution step-by-step.
Andre buys a total of 5 pounds of snacks, which include apricots and dried bananas. He spends a total of [tex]$24.50. We need to find out how many pounds of apricots and dried bananas he bought.
Let's define:
- \( a \) as the pounds of apricots.
- \( b \) as the pounds of dried bananas.
We have two pieces of information that we can use to form a system of equations:
1. The total weight of snacks:
\( a + b = 5 \)
This equation represents the total number of pounds of apricots and dried bananas he bought, which is 5 pounds.
2. The total cost of the snacks:
\( 6a + 4b = 24.50 \)
This equation comes from the fact that apricots cost $[/tex]6 per pound and dried bananas cost [tex]$4 per pound. So, in total, Andre spent $[/tex]24.50.
Now, let's solve the system of equations:
1. From the first equation, express [tex]\( b \)[/tex] in terms of [tex]\( a \)[/tex]:
[tex]\[
b = 5 - a
\][/tex]
2. Substitute [tex]\( b = 5 - a \)[/tex] into the second equation:
[tex]\[
6a + 4(5 - a) = 24.50
\][/tex]
3. Distribute the 4:
[tex]\[
6a + 20 - 4a = 24.50
\][/tex]
4. Combine like terms:
[tex]\[
2a + 20 = 24.50
\][/tex]
5. Subtract 20 from both sides:
[tex]\[
2a = 4.50
\][/tex]
6. Divide both sides by 2 to solve for [tex]\( a \)[/tex]:
[tex]\[
a = 2.25
\][/tex]
Having found [tex]\( a = 2.25 \)[/tex], substitute back to find [tex]\( b \)[/tex]:
7. Substitute [tex]\( a = 2.25 \)[/tex] into [tex]\( b = 5 - a \)[/tex]:
[tex]\[
b = 5 - 2.25 = 2.75
\][/tex]
So, Andre bought 2.25 pounds of apricots and 2.75 pounds of dried bananas.
Andre buys a total of 5 pounds of snacks, which include apricots and dried bananas. He spends a total of [tex]$24.50. We need to find out how many pounds of apricots and dried bananas he bought.
Let's define:
- \( a \) as the pounds of apricots.
- \( b \) as the pounds of dried bananas.
We have two pieces of information that we can use to form a system of equations:
1. The total weight of snacks:
\( a + b = 5 \)
This equation represents the total number of pounds of apricots and dried bananas he bought, which is 5 pounds.
2. The total cost of the snacks:
\( 6a + 4b = 24.50 \)
This equation comes from the fact that apricots cost $[/tex]6 per pound and dried bananas cost [tex]$4 per pound. So, in total, Andre spent $[/tex]24.50.
Now, let's solve the system of equations:
1. From the first equation, express [tex]\( b \)[/tex] in terms of [tex]\( a \)[/tex]:
[tex]\[
b = 5 - a
\][/tex]
2. Substitute [tex]\( b = 5 - a \)[/tex] into the second equation:
[tex]\[
6a + 4(5 - a) = 24.50
\][/tex]
3. Distribute the 4:
[tex]\[
6a + 20 - 4a = 24.50
\][/tex]
4. Combine like terms:
[tex]\[
2a + 20 = 24.50
\][/tex]
5. Subtract 20 from both sides:
[tex]\[
2a = 4.50
\][/tex]
6. Divide both sides by 2 to solve for [tex]\( a \)[/tex]:
[tex]\[
a = 2.25
\][/tex]
Having found [tex]\( a = 2.25 \)[/tex], substitute back to find [tex]\( b \)[/tex]:
7. Substitute [tex]\( a = 2.25 \)[/tex] into [tex]\( b = 5 - a \)[/tex]:
[tex]\[
b = 5 - 2.25 = 2.75
\][/tex]
So, Andre bought 2.25 pounds of apricots and 2.75 pounds of dried bananas.
