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Answer :
Answer:
(a)
[tex]3b + 4g =10.25[/tex]
[tex]2b + 2g = 5.50[/tex]
(b)
1 pound of banana = $0.75
1 pound of grape = $2.00
Step-by-step explanation:
Given
Represent banana with b and grapes with g.
From the first statement, we have:
[tex]3b + 4g =10.25[/tex]
From the second, we have:
[tex]2b + 2g = 5.50[/tex]
Solving (a): The equations
This has been solved above.
The equations are:
[tex]3b + 4g =10.25[/tex]
[tex]2b + 2g = 5.50[/tex]
Solving (b):
[tex]3b + 4g =10.25[/tex] --- (1)
[tex]2b + 2g = 5.50[/tex] --- (2)
Multiply (2) by 2
[tex]2b + 2g = 5.50[/tex] * 2
[tex]4b + 4g = 11[/tex] ----- (3)
Subtract (3) from (1)
[tex]3b - 4b + 4g - 4g = 10.25 - 11[/tex]
[tex]-b =-0.75[/tex]
[tex]b =0.75[/tex]
Substitute 0.75 for b in (2)
[tex]2b + 2g = 5.50[/tex]
[tex]2 *0.75 + 2g = 5.5[/tex]
[tex]1.5 + 2g = 5.5[/tex]
Collect Like Terms
[tex]2g = 5.5 - 1.5[/tex]
[tex]2g = 4[/tex]
[tex]g = 2[/tex]
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