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nasty-shy [4]
3 years ago
10

Clayton has $500 in his retirement account, and Jason has $400 in his. Clayton is adding $10 per day, whereas Jason is contribut

ing $12 per day. Eventually, the two accounts will contain the same amount. What balance will each account have?
Mathematics
1 answer:
daser333 [38]3 years ago
6 0

Answer:

$1000

Step-by-step explanation:

We can form an equation for Clayton's account: C = 500 + 10x

We can form an equation for Clayton's account:  J = 400 +12x  

(where x is the number of days)

When the two accounts will contain the same amount, it means: C = J

<=> 500 + 10x  = 400 +12x  

<=> x =50

After 50 days, there accounts will be balance. Then, we substitue x into any of the 2 equation to find out the amount: 500 + 10(50) = $1000

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Whereby ∠DAB is bisected by AG and ∠ABC is bisected by BH

Therefore, ∠GAB + ∠HBA = 90°

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∴ ∠AGD = ∠AGD since ∠AGD = ∠GAB (Bisected angle)

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Hence ΔDAQ  ≅ ΔDGQ ≅ ΔGPH and AQ = QG = GP

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\angle GAB = cos^{-1} \left (\dfrac{36}{39}  \right )

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GH = 13 in.

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The height of the parallelogram = AD × sin(∠DAB) =  13 × sin(45.24°)

The height of the parallelogram = 120/13 =  9.23 in.

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