At the beginning of the season, MacDonald had to remove
\[5\] orange trees from his farm. Each of the remaining trees produced
\[210\] oranges for a total harvest of
\[41790\] oranges.
Write an equation to determine the initial number of orange trees
\[(t)\] on MacDonald's farm.
Find the initial number of orange trees on MacDonald's farm.
orange trees
Let's assume the initial number of orange trees on MacDonald's farm is \( t \).
According to the problem, MacDonald removed 5 orange trees, so the number of trees remaining after the removal is \( t - 5 \).
Each of the remaining trees produced 210 oranges, so the total number of oranges from the remaining trees is \( 210(t-5) \).
The problem also states that the total harvest was 41790 oranges. So, we can write the equation:
\( 210(t-5) = 41790 \)
To find the initial number of orange trees, we can solve this equation for \( t \):
\( 210t - 1050 = 41790 \)
\( 210t = 42840 \)
\( t = \frac{42840}{210} \)
\( t \approx 204 \)
So, the initial number of orange trees on MacDonald's farm was approximately 204.
Raymond just got done jumping at Super Bounce Trampoline Center. The total cost of his session was
\[\$43.25\]. He had to pay a
\[\$7\] entrance fee and
\[\$1.25\] for every minute he was on the trampoline.
Write an equation to determine the number of minutes
\[(t)\] that Raymond was on the trampoline.
Find the number of minutes he was on the trampoline.
minutes
Let's assume the number of minutes Raymond was on the trampoline is \( t \).
According to the problem, Raymond had to pay a $7 entrance fee and $1.25 for every minute he was on the trampoline. So, the total cost of his session can be represented by the equation:
\( 7 + 1.25t = 43.25 \)
To find the number of minutes he was on the trampoline, we can solve this equation for \( t \):
\( 1.25t = 43.25 - 7 \)
\( 1.25t = 36.25 \)
\( t = \frac{36.25}{1.25} \)
\( t = 29 \)
So, Raymond was on the trampoline for 29 minutes.
Cookies are on sale! Today each cookie costs
\[\$0.75\] less than the normal price. Right now if you buy
\[7\] of them it will only cost you
\[\$2.80\]!
Write an equation to determine the normal price of each cookie
\[(c)\].
Find the normal price of each cookie.
\[\$\]
Let's assume the normal price of each cookie is \( c \).
According to the problem, each cookie costs $0.75 less than the normal price. Therefore, the sale price of each cookie is \( c - 0.75 \).
If you buy 7 cookies, it will only cost you $2.80. So, we can write the equation:
\( 7(c-0.75) = 2.80 \)
To find the normal price of each cookie, we can solve this equation for \( c \):
\( 7c - 5.25 = 2.80 \)
\( 7c = 7.05 \)
\( c = \frac{7.05}{7} \)
\( c \approx 1 \)
Therefore, the normal price of each cookie is approximately $1.
To find the initial number of orange trees on MacDonald's farm, we can set up an equation using the given information.
Let's assume that the initial number of orange trees on MacDonald's farm is t.
We know that MacDonald removed 5 orange trees from his farm, so the number of remaining trees would be (t - 5).
Each remaining tree produced 210 oranges, so the total number of oranges harvested would be (t - 5) * 210.
Given that the total number of oranges harvested is 41790, we can set up the equation:
(t - 5) * 210 = 41790
To solve this equation for t, we can divide both sides by 210:
(t - 5) = 41790 / 210
Simplifying the right side:
(t - 5) = 199
Now, let's solve for t by adding 5 to both sides:
t = 199 + 5
t = 204
Therefore, the initial number of orange trees on MacDonald's farm was 204.