I have trouble with world problems and three especially are giving me grief, can anyone verify my answers?
First:
The length of a yard is triple the length of the garden. Write the expression for the difference between the length of the yard and the length of garden.
(a) Define the variable being used. (b) Write the expression given in the problem; do not simplify at this step.
(c) Simplify the expression.
A: Y=yard G=garden
B: Y-G=3G-G
C: 2G
Second Question
Tina received 2000 fewer votes than Michael in an election. Samantha received 4200 more votes than Michael in the election. Write the expression for the number of votes received by Samantha plus the number of votes received by Michael minus the number of votes received by Tina.
(a) Define the variable being used.
(b) Write the expression given in the problem; do not simplify at this step.
(c) Simplify the expression.
A: M-2000=T M+4200=S
B: S+M-T= M+4200+M-(M-2000) = M+4200+M-M+2000
C: M+6200
Final question:
A gold bracelet costs $130 less than a gold necklace. A gold locket costs $60 more than the gold necklace. Write the expression for the price of the bracelet plus the price of the necklace minus the price of the locket.
For this project, please translate the word problems below using the given directions.
(a) Define the variable being used.
(b) Write the expression given in the problem; do not simplify at this step.
(c) Simplify the expression.
A: B = N-130 L = N+60
B: N-130+N+60-L
C: 2N-70-L
Thank you so much for verifying or explaining where I went may have went wrong.
1.
It said: "The length of a yard is triple the length of the garden"
--> so if you let the length of the garden be x
then the length of the yard is 3x
(we could have used any variable name, you used G, that's fine)
It said: "the difference between the length of the yard and the length of garden
difference means "subtract" , so
3x - x
= 2x
2. I did this for you in the other post
3. cost of gold necklace---- x
cost of gold bracelet = x - 130
cost of gold locket = x+60
price of the bracelet plus the price of the necklace minus the price of the locket
= (price of the bracelet) + (the price of the necklace) - (the price of the locket)
= (x-130) + x - (x+60)
= x-130+x-x-60
= x - 190
Let's go through each question step by step and verify your answers:
First Question:
(a) The variable being used is G for the length of the garden.
(b) The expression given in the problem is Y - G, where Y represents the length of the yard.
(c) To simplify the expression, we substitute Y with 3G (since the length of the yard is triple the length of the garden): 3G - G = 2G.
Your answer for this question is correct.
Second Question:
(a) The variable being used are M for Michael's votes, T for Tina's votes, and S for Samantha's votes.
(b) The expression given in the problem is S + M - T.
(c) To simplify the expression, we substitute S with M + 4200 (since Samantha received 4200 more votes than Michael) and T with M - 2000 (since Tina received 2000 fewer votes than Michael): (M + 4200) + M - (M - 2000) = M + 4200 + M - M + 2000.
Simplifying this further, we get M + 4200 + 2000 = M + 6200.
Your answer for this question is correct.
Final Question:
(a) The variable being used are N for the price of the necklace, B for the price of the bracelet, and L for the price of the locket.
(b) The expression given in the problem is B + N - L.
(c) To simplify the expression, we substitute B with N - 130 (since the bracelet costs $130 less than the necklace) and L with N + 60 (since the locket costs $60 more than the necklace): (N - 130) + N - (N + 60) = N - 130 + N - N - 60.
Simplifying this further, we get 2N - 190.
It appears you made a mistake in your simplified expression for the final question. The correct answer is 2N - 190, not 2N - 70 - L.
Overall, you did a great job with these world problems, and I have verified the correct answers for you. Keep practicing, and you'll become even more proficient at solving such problems!