Question

Laci and Leon are saving money to go to an amusement park. Laci has $1 more than 4 times the amount of money Leon has. Together, they have $76. Write an equation to determine how much money they have together.

Answer 1

5 x+1=75....equation 1

amount saved by Laci=$61

amount saved by Leon=$15

Explanation:

Step 1

Express the total amount of money saved by each person as shown;

Let the amount of money saved be;

Leon=x

Laci=4 times as Leon plus 1=4×x+1=4 x+1

Total amount saved=$76

Step 2

Express the total amount saved by all of them as shown;

Total amount saved=amount saved by Leon+amount saved by Laci

where;

Total amount saved=$76

amount saved by Leon=x

amount saved by Laci=4 x+1

replacing;

76=x+4 x+1

5 x+1=75....equation 1

76=5 x+1

5 x=76-1

5 x=75

x=75/5

x=15

Step 3

Substitute the value of x to get the amount of money spent by both Leon and Laci;

amount saved by Leon=x=15

amount saved by Laci=4 x+1=(4×15)+1=61

Answer 2

Laci has $61 and Leon has $15.

Explanation:

Givens:

• Laci has $1 more than 4 times Leon.
• They have together $76.

So,
`La` is Laci, and
`Le` is Leon.

So, according to the problem:

`La=4Le +1`

Because Laci has $1 more than 4 times Leon's money.

Then,

`La+Le=76`

Because together they have $76.

Now, we replace the first equation in the second one:

`4Le +1+Le=76`

`5Le=76-1`

`5Le=75`

`Le=(75)/(5)=15`

Replacing this value in the first equation:

`La=4Le +1`

`La=4(15) +1=61`

Therefore, Laci has $61 and Leon has $15. The expression that models this problem is a system of equations formed by:

`La=4Le +1`

`La+Le=76`