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Nezavi [6.7K]
2 years ago
14

Se tiene el mismo número de cajas de manzanas que de limones. Si en una caja de manzanas caben 13 unidades y en una de limones c

aben 17, ¿cuántas cajas de cada tipo de fruta se tienen si hay un total de 180 frutas?
Mathematics
2 answers:
Mandarinka [93]2 years ago
8 0

Answer:

\large \boxed{\text{6 boxes of apples and 6 boxes of lemons}}

Step-by-step explanation:

     Let m = the number of boxes of apples. Then

        13m = the number of apples

       Let l = the number of boxes of lemons. Then  

          17l = the number of lemons and

13m + 17l = the total number of fruits

You have two conditions:

\begin{array}{rrclr}(1) & m & = &l\\(2) & 13m + 17l & = & 180\\\end{array}

Solve the equations for m and l

\begin{array}{rrcll}(1) & m & = & l&\\(2) & 13m + 17l & = & 180\\(3)&13m +17m & = & 180 & \text{Substituted (1) into (2)}\\&30m& = &180 &\text{Simplified}\\(4)&m& = &\mathbf{6} &\text{Divided each side by 30}\\& 6& = &l& \text{Substituted (4) into (1)}\\& l& = &\mathbf{6}& \\\end{array}\\\text{You have $\large \boxed{\textbf{6 boxes of apples and 6 boxes of lemons}}$}

Check:

\begin{array}{ccc}6 = 6 & \qquad & 13(6) + 17(6) = 180\\& \qquad & 78 + 102 =180\\& \qquad & 180 = 180\\\end{array}

It checks.

sattari [20]2 years ago
7 0

Answer: 6 cajas de cada tipo de fruta.

Step-by-step explanation:

En cada caja de manzanas, tenemos 13 manzanas.

En cada caja de limones, tenemos 17 limones.

Si el numero total de cajas es C, entonces el numero total de manzanas es:

C*13

y el numero total de limones es: C*17.

Si en total tenemos 180 frutas, entonces tenemos que:

C*13 + C*17 = 180

C*(13 + 17) = 180

C*30 = 180

C = 180/30 = 6

Tenemos 6 cajas de cada tipo de fruta.

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