Beth had $130 more than Casper at first. After Casper spent $21, Beth had 5 times as much as money as Casper. How much did Beth have?

Question

Beth had  $130 more than Casper at first. After Casper spent  $21, Beth had 5 times as much as money as Casper. How much did Beth have?

Bytelearn · Accepted Answer

Initial Equation Setup: Let's denote Beth's initial amount of money as B and Casper's initial amount of money as C. According to the problem, Beth had $130 more than Casper at first. We can write this as an equation: B = C + $130Casper's Expenditure: After Casper spent $21, his new amount of money is C - $21. At this point, Beth has 5 times as much money as Casper. We can write this as another equation: B = 5 * (C - $21)Substitution and Simplification: Now we have two equations with two variables. We can solve these equations simultaneously. From the first equation, we substitute B in the second equation with C + $130: C + $130 = 5 * (C - $21)Solving for Casper's Amount: Let's solve for C: C + $130 = 5C - 5 * $21 C + $130 = 5C - $105 Now, we bring all terms involving C to one side and constants to the other side: $130 + $105 = 5C - C $235 = 4CFinding Beth's Amount: Divide both sides by 4 to find the value of C: $235 / 4 = C $58.75 = C Casper initially had $58.75.Now that we know Casper's initial amount, we can find Beth's initial amount using the first equation: B = C + $130 B = $58.75 + $130 B = $188.75 Beth initially had $188.75.

Beth had $\$ 130$ more than Casper at first. After Casper spent $\$ 21$ , Beth had $5$ times as much as money as Casper. How much did Beth have?

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Beth had $\$ 130$ more than Casper at first. After Casper spent $\$ 21$ , Beth had $5$ times as much as money as Casper. How much did Beth have?