High School

Linda saves $1.55 every day. Tyron saves $3.90 every day. Linda started saving 3 days earlier than Tyron. On which day will Tyron's savings be more than Linda's savings?

Answer :

To determine when Tyron's savings will surpass Linda's, we can set up an inequality using their daily saving rates and the fact that Linda started 3 days earlier. Solving for the number of days Tyron needs to save, we find that Tyron will surpass Linda's savings after saving for 2 full days.

Linda and Tyron are saving money on a daily basis, but Linda started saving 3 days earlier than Tyron. To find out on which day Tyron's savings will be more than Linda's, we need to set up an equation.

Let's define x as the number of days after which Tyron starts saving. Since Linda starts 3 days earlier, she has been saving for x + 3 days by the time Tyron starts saving.

Linda's daily savings: $1.55
Tyron's daily savings: $3.90

Linda's total savings after x + 3 days: $1.55(x + 3)
Tyron's total savings after x days: $3.90x

We want to find the value of x at which Tyron's total savings exceed Linda's, so we set up the inequality:
$3.90x > $1.55(x + 3)

Now, solve for x:

$3.90x > $1.55x + $4.65
$3.90x - $1.55x > $4.65
$2.35x > $4.65
x > $4.65 / $2.35
x > 1.978

Since x represents the number of days and we cannot have a fraction of a day in this context, x must be at least 2 days. Therefore, Tyron's savings will be more than Linda's after he has saved for 2 days.
Step 1: Write the amount of savings in equation
Linda's savings: s=1.55d
Tyron's savings: m=3.90d

Step 2: Add on the extra days to Linda's savings
Linda's savings s=1.55d+3(1.55)

Step 4: Simplify equation
s=1.55d+3(1.55)
s=1.55d+4.66

Step 5: Substitute numbers for d days until Tyron's m savings is greater than Linda's s saving
m=3.90d s=1.55(2)+4.66
m=3.90(2) s=3.10+4.66
m=7.80 s=7.76

On Tyron's second day he will have more money in his savings than Linda does.