need help on story problem for 8th grade math

Question

1-Monica bought 3 types of fruit for a fruit salad. She paid twice as much for blueberries as for oranges, and 1.50$ less for strawberries than for blueberries. If the total cost was $12.25 how much did Monica spend on each type of fruit?

 

 

 

2- Tommy give baseball cards to four of his friends. He gives Kiana 3 cards less than he gives Gary. He gives Monty 7 cards more than he gives Kiana. He gives Willa twice as many as he gives Monty. How many cards does Tommy give to each friend if he gives out a total of 74 cards?

Answer 1

Dear Chris,

     These two problems are very much alike.  "Total" means add everything together.

 

Let X = number of oranges

 

blueberries =2X              There are twice as many blueberries as oranges.

 

strawberries= 2X-$1.5     Strawberries are $1.5 less than the price of blueberries.

 

total= $12.25

 

1X + 2X + 2X- 1.5 =12.25  collect terms

 

5X - 1.5 = 12.25               Now, you want to solve for "X," so what will you do to both sides of the

 

equation?

5X -1.5 +1.5 = 12.25 +1.5                  5X= 13.75       Divide by number next to "X."

How much was each type of fruit?

 

X=_____________  number of oranges                 2X= ________number of blueberries                

 

2X-$1.50=____________

strawberries                         

 

 

Don' t forget to check your work by substituting into the following equation:

 

1X + 2X + 2X- 1.5 =12.25                                                                                                          

 

 

 

X= $2.75

 

If you like my work and I was helpful, please give me a thumbs up.

                                                                      Susan C.

 

Answer 2

Hi Chris,

 

1- Let X = the cost of oranges

 

She paid twice as much for blueberries as oranges--> 2X = cost of blueberries

 

She paid $1.50 less for strawberries than blueberries--> 2X - 1.5 = cost of strawberries

 

The total cost was 12.25--> X + 2X + 2X - 1.5 = 12.25

 

Combine like terms--> 5X = 13.75

 

Divide both sides by 5--> X = $2.75 = cost of oranges

 

Then $5.50 = cost of blueberries and $4.00 = cost of starwberries

 

Check and see if they add up to $12.25

 

2- Let X = number of cards for Gary

 

Kiana gets 3 fewer cards--> X -3

 

Monty gets 7 more cards than Kiana--> X - 3 + 7

 

Willa gets twice as many cards as Monty--> 2(X -3 + 7)

 

total of 74 cards--> X + X - 3 + X - 3 + 7 + 2(X - 3 + 7) = 74

 

Multiply 2 times what's in the parentheses and start combining like terms--> 3X + 1 + 2X - 6 + 14 = 74

 

Continue combining like terms--> 5X = 65

 

Divide both sides by 5--> X = 13 = Gary.

 

Then Kiana = 10 and Monty = 17 and Willa = 34

 

Now add them up to see if it comes to 74.

 

Dan