Question

Mario and Luigi are comparing how many coins they found today. Mario found 10 more coins than Luigi. The two of them found 88 coins combined.
Let M represent the number of Mario's coins and L represent the number of Luigi's coins.

Write a system of equations to represent the scenario above.



(1 point)
Responses

{M=L+10M+L=88

{L=M+88M+L+10=0

{88=L+10M−L=88

Mario found 80 coins, Luigi found 8 coins
Mario found 80 coins, Luigi found 8 coins

Mario found 49 coins, Luigi found 39 coins

Answer 1

To represent the scenario mathematically, we can set up the following system of equations based on the information given:

1. Mario found 10 more coins than Luigi:
\( M = L + 10 \)

2. The total number of coins they found together is 88:
\( M + L = 88 \)

So the system of equations is:
\[
\begin{cases}
M = L + 10 \\
M + L = 88
\end{cases}
\]

Now, let's check the options to see which one matches our equation system. The correct response is:
\(\{ M = L + 10, M + L = 88 \}\)

Now, we can confirm their individual coin counts by solving this system of equations.

Substituting the first equation into the second:
\( (L + 10) + L = 88 \)
\( 2L + 10 = 88 \)
\( 2L = 78 \)
\( L = 39 \)

Now, substituting \(L\) back to find \(M\):
\( M = L + 10 = 39 + 10 = 49 \)

Thus, Mario found 49 coins, and Luigi found 39 coins.

The option corresponding to this solution is:
Mario found 49 coins, Luigi found 39 coins.