Drag the tiles to the correct boxes to complete the pairs. Match each word problem to its solution Word problems:
"Seven more than 3 times a number is 49. What is the number?"
"Hillary's age is 2/3 times Lily's age.if Hillary is 19 years old, how old is Lily?"
"Twice a number decreased by 20 is 50. What is the number?"
"Claret purchased two handbags and a wallet. The cost of each handbag was $10 more than the wallet. If she had a total of $60 for the two handbags, what is the cost of the wallet?"
Answers:
35
20
14
24

A) 14

B)24

C)35

D)20

Step-by-step explanation:

A) Let the number be x.

Thus, 3x + 7 = 49

3x = 49 - 7

3x = 42

x = 42/3

x = 14

B) let lily's age be y.

Since Hillary's age is 19 years.

So,

19 = ⅔y + 3

⅔y = 19 - 3

⅔y = 16

Multiply both sides by 3 to give ;

2y = 48

y = 48/2

y = 24.

Lilly's age = 24 years

C) let the number be z.

Thus,

2z - 20 = 50

2z = 50 + 20

2z = 70

z = 70/2

z = 35

D) Let the cost of the handbag be p and the cost of the wallet be q.

Each handbag costs $10 more than each wallet.

Thus;

Cost of handbag = p + 10

Since she bought 2 handbags and a wallet and spent a total of $60 on the handbags.

Thus;

2(p + 10) = 60

2p + 20 = 60

2p = 60 - 20

2p = 40

p = 40/2

p = $20

To get the other factor of the expression x² - 10x + 24, we can use long or synthetic division. We are given that the other factor is x - 6, so we can use that as our divisor. Our setup should look something like this:
x² - 10x + 24 ÷ x - 6
Here is the work using polynomial long division:
          x     -4             
x - 6 | x² - 10x + 24
          x² - 6x
          0  - 4x + 24
               -4x - 24
                          0
We can see that our quotient is x - 4, which would be the other factor of x - 6 to get x² - 10x + 24. The answer to your query is x - 4. Hope this helps and have a phenomenal day!