Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks. Vicky and Diana each opened a savings account on the same day. Vicky started by putting $404 in her account, and she will deposit an additional $188 each week. Diana made an initial deposit of $442, and she will add $186 more each week. Eventually, Vicky and Diana will each have the same amount saved. What is that amount? How many weeks will that take? Vicky and Diana will each have saved a total of $_____ after _____ weeks.

Question

Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks.  Vicky and Diana each opened a savings account on the same day. Vicky started by putting $404 in her account, and she will deposit an additional $188 each week. Diana made an initial deposit of $442, and she will add $186 more each week. Eventually, Vicky and Diana will each have the same amount saved. What is that amount? How many weeks will that take?   Vicky and Diana will each have saved a total of $_____ after _____ weeks.

Bytelearn · Accepted Answer

Define Equations:  Step 1: Define the equations based on the problem statement. Vicky's savings after t weeks: V(t) = 404 + 188t Diana's savings after t weeks: D(t) = 442 + 186t We need to find when V(t) = D(t). Set Up Equation:  Step 2: Set up the equation to find when their savings are equal. 404 + 188t = 442 + 186t Subtract 186t from both sides: 188t - 186t = 442 - 404 Simplify: 2t = 38 Solve for t:  Step 3: Solve for t. Divide both sides by 2: t = 38 / 2 t = 19 weeks. Substitute and Calculate:  Step 4: Substitute t back into either V(t) or D(t) to find the amount saved. Using V(t): V(19) = 404 + 188 * 19 Calculate: V(19) = 404 + 3572 V(19) = 3976 dollars.

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