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Lisa is weighing combinations of children’s blocks. Four blue blocks and five red blocks weigh 32 ounces. One blue block and eight red blocks weigh 35 ounces. What is the combined weight of one red block and one blue block?

Respuesta :

JeanaShupp

Answer: 7 ounces

Step-by-step explanation:

Let x = Weight of one blue block.

y = Weight of one red block.

As per given , we have the following system of equation:

[tex]4x+5y=32 ---------------(1)\\\\ x+8y=35 ---------------(2)[/tex]

Multiply 4 to equation (2) , we get

[tex]4x+32y=140-------(3)[/tex]

Eliminate (1) from (3) , we get

[tex]27y=108\\\\ y=\dfrac{108}{27}\\\\ y=4[/tex]

i.e.  Weight of one red block = 4 ounces

Put value of y in (2) , we get

[tex]x+8(4)=35\\\\ x=35-32\\\\ x=3[/tex]

i.e.  Weight of one blue block = 3 ounces

The combined weight of one red block and one blue block = 4+3 = 7 ounces

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