Marty has a box of raisins. he uses 1 1/2 cups of raisins for trail mix. then he opens a bag with 2 1/3 cups of raisins in it. marty then uses 3/4 cup of raisins for bread pudding. there are 3 1/2 cups of raisins left. how many cups of raisins were in the box. explain.

Step-by-step explanation:

Let

x------> cups of raisins originally in the box

we know that

The original quantity is equal to the quantity that is left plus the quantity used

so

Convert mixed number to an improper fraction

substitute

Step-by-step explanation:

x=box raisins

Total raisins = raisins used plus raisins left

x+7/3 = 3/2+3/4+7/2

x-7/3+7/3 = 3/2+7/2+3/4-7/3

x = 10/2 + 3/4 - 7/3

Find GCF

x = 6/6*10/2 + 3/3*3/4 - 4/4*7/3

x = 60/12 + 9/12 - 28/12

x = 69/12 - 28/12

x = 41/12

x = 3-5/12 cups raisins in the box

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21.4 i did it already for s1

step-by-step explanation:

m∠cdf = 43° , m∠gdf = 114°, m∠gde = 23°, m∠edh = 23° , m∠cdh = 157°

step-by-step explanation:

since, it is given that de bisects the angle gdh ⇒ de divides the angle gdh into two equal angles.

⇒ m∠gde = m∠edh

⇒ 8·x   - 1 = 6·x + 5

⇒ x = 3

so, m∠gde = 8·x - 1 = 23°

and m∠edh = 23°

now, it is given ∠cde is an straight angle so, m∠cde = 180°

⇒ m∠cdf + m∠fdg + m∠gde = 180°

⇒ 43° + m∠fdg + 23° = 180°

⇒ m∠fdg = 114°

again, m∠cde = m∠cdh + m∠edh = 180°

m∠cdh + 23° = 180°

⇒ m∠cdh = 157°