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Answer :
Sure! Let's solve this problem step-by-step:
1. Define your variables:
- Let [tex]\( a \)[/tex] represent the number of pounds of apricots.
- Let [tex]\( b \)[/tex] represent the number of pounds of bananas.
2. Set up the system of equations:
- The first equation comes from the total weight of the snacks:
[tex]\[
a + b = 5
\][/tex]
This equation represents the fact that Andre buys a total of 5 pounds of snacks.
- The second equation comes from the total cost of the snacks:
[tex]\[
6a + 4b = 24.50
\][/tex]
This equation represents the total cost, where apricots cost [tex]$6 per pound and bananas $[/tex]4 per pound, and the total spending is $24.50.
3. Solve the system of equations:
- Start with the first equation to express one variable in terms of the other. Let's solve for [tex]\( b \)[/tex]:
[tex]\[
b = 5 - a
\][/tex]
- Substitute [tex]\( b = 5 - a \)[/tex] into the second equation:
[tex]\[
6a + 4(5 - a) = 24.50
\][/tex]
- Distribute and simplify:
[tex]\[
6a + 20 - 4a = 24.50
\][/tex]
- Combine like terms:
[tex]\[
2a + 20 = 24.50
\][/tex]
- Solve for [tex]\( a \)[/tex]:
[tex]\[
2a = 24.50 - 20
\][/tex]
[tex]\[
2a = 4.50
\][/tex]
[tex]\[
a = 2.25
\][/tex]
- Now, substitute back to find [tex]\( b \)[/tex]:
[tex]\[
b = 5 - a = 5 - 2.25 = 2.75
\][/tex]
4. Conclusion:
- Andre bought 2.25 pounds of apricots and 2.75 pounds of bananas.
1. Define your variables:
- Let [tex]\( a \)[/tex] represent the number of pounds of apricots.
- Let [tex]\( b \)[/tex] represent the number of pounds of bananas.
2. Set up the system of equations:
- The first equation comes from the total weight of the snacks:
[tex]\[
a + b = 5
\][/tex]
This equation represents the fact that Andre buys a total of 5 pounds of snacks.
- The second equation comes from the total cost of the snacks:
[tex]\[
6a + 4b = 24.50
\][/tex]
This equation represents the total cost, where apricots cost [tex]$6 per pound and bananas $[/tex]4 per pound, and the total spending is $24.50.
3. Solve the system of equations:
- Start with the first equation to express one variable in terms of the other. Let's solve for [tex]\( b \)[/tex]:
[tex]\[
b = 5 - a
\][/tex]
- Substitute [tex]\( b = 5 - a \)[/tex] into the second equation:
[tex]\[
6a + 4(5 - a) = 24.50
\][/tex]
- Distribute and simplify:
[tex]\[
6a + 20 - 4a = 24.50
\][/tex]
- Combine like terms:
[tex]\[
2a + 20 = 24.50
\][/tex]
- Solve for [tex]\( a \)[/tex]:
[tex]\[
2a = 24.50 - 20
\][/tex]
[tex]\[
2a = 4.50
\][/tex]
[tex]\[
a = 2.25
\][/tex]
- Now, substitute back to find [tex]\( b \)[/tex]:
[tex]\[
b = 5 - a = 5 - 2.25 = 2.75
\][/tex]
4. Conclusion:
- Andre bought 2.25 pounds of apricots and 2.75 pounds of bananas.
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