Liam deposits l dollars into an account that earns 0.9% in simple interest each year. Grace deposits g dollars into an account that earns 1.1% in simple interest each year. Both Liam and Grace let their money earn interest for one year and make no further deposits. If Liam's initial deposit was $800 more than Grace's, and if both Liam and Grace earn the same amount of interest after one year, which of the following systems of equations could be used to find their initial deposits? Choose 1 answer: (A) 0.009 l+800=0.011 g l=g (B) 0.009 l=0.011 g+800 l=g (c) 0.009 l=0.011 g l+800=g (D) 0.009 l=0.011 g l=g+800

Question

Liam deposits  l dollars into an account that earns  0.9% in simple interest each year. Grace deposits  g dollars into an account that earns  1.1% in simple interest each year. Both Liam and Grace let their money earn interest for one year and make no further deposits. If Liam's initial deposit was  $800 more than Grace's, and if both Liam and Grace earn the same amount of interest after one year, which of the following systems of equations could be used to find their initial deposits? Choose 1 answer: (A)  0.009 l+800=0.011 g  l=g (B)  0.009 l=0.011 g+800  l=g (c)  0.009 l=0.011 g  l+800=g (D)  0.009 l=0.011 g  l=g+800

Bytelearn · Accepted Answer

Set Up Equations:  Step 1: Let's set up the equations based on the information given. Liam's deposit is l dollars and Grace's deposit is g dollars. Liam's deposit is $800 more than Grace's, so we have l = g + 800. Calculate Interest:  Step 2: Now, let's calculate the interest earned by both after one year. Liam earns 0.9% interest, so his interest is 0.009l. Grace earns 1.1% interest, so her interest is 0.011g. They both earn the same amount of interest, so we have 0.009l = 0.011g. Solve Equations:  Step 3: We now have two equations: 1) l = g + 800 2) 0.009l = 0.011g We need to find which answer choice matches our equations. Check Answer Choices:  Step 4: Let's check the answer choices. Choice (A) says 0.009l + 800 = 0.011g and l = g, which doesn't match our equations. Choice (B) says 0.009l = 0.011g + 800 and l = g, which also doesn't match. Choice (C) says 0.009l = 0.011g and l + 800 = g, which is incorrect. Choice (D) says 0.009l = 0.011g and l = g + 800, which matches our equations exactly.

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