Question

Each costume needs 46 centimeters of red ribbon and 3 times as much yellow ribbon. What is the total length ribbon for 64 costumes? Express your answer in meters.
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When making a batch of orange juice for her basketball team, Jackie used 5 times as much water as concentrate. There were 32 more cups of water than concentrate.

A: How much juice did she make in all?

B: She poured the juice into quart containers. How many containers could she fill?

Answer 1

1=138+46=184
184x64=11,776
11776 divided by 100=117.76

A=8
B=12

Answer 2

1. the total length ribbon for 64 costumes : 117.76 m

2. A. 48 cups juice

B. 12 quarts container

Further Explanation  

One variable linear equation is an equation that has a variable and the exponent number is one.  

Can be stated in the form:  

$\large{\boxed{\bold{ax=b}}$

or  

ax + b = c, where a, b, and c are constants, x is a variable  

Whereas the two-variable linear equation is a linear equation that has 2 variables and the exponent is one  

Can be stated in the form:  

$\large{\boxed{\bold{ax+bx=c}}}$

x, y = variable  

1. Each costume needs 46 centimeters of red ribbon and 3 times as much yellow ribbon

If we translate this sentence into equation:

C(costume) = red ribbon + yellow ribbon

C(costume) = red ribbon + (3 x red ribbon)

C(costume)= 46 + 3.(46)

C(costume) = 184 cm

So total ribbon for each costume = 184 cm

Then, for 64 costume will need :

64 x 184 cm = 11776 cm

We convert to m :

1 cm = 10⁻² m

11776 cm = $\large{\boxed{\bold{117.76\:m}}}$

2.

Let C = cups of concentrate

W = cups of water

Jackie used 5 times as much water as concentrate.

If we translate this sentence into equation:

5W(water) = C(concentrate)

W = 5C  .. equation 1

There were 32 more cups of water than concentrate.

If we translate this sentence into equation:

W = 32+C .. equation 2

From equation 1 dan 2 :

5C= 32 + C

4C = 32

C = 8 cups

W = 5 x 8

W = 40 cups

A. Total juice she can make :

= 40 + 8 cups

= $\large{\boxed{\bold{48\:cups}}}$

B. The units for US standart volume

1 gallon = 4 quarts = 8 pints = 16 cups = 128 fluid ounces

so 1 cups = 0.25 quarts

then for 48 cups :

= 48 x 0.25 quarts

= $\large{\boxed{\bold{12\:quarts}}}$