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Math  /  Algebra

Question1 Fill in the Blank 5 points
Jenna intends on baking an apple pie and a sweet potato pie for Thanksgiving. She spends $10\$ 10 purchasing apples and sweet potatoes. Suppose apples cost \1.25each,andsweetpotatoescost1.25 each, and sweet potatoes cost \1 1 each. Let aa represent the number of apples she purchases, and ss represent the number of sweet potatoes she purchases. a) Write an equation in standard form that describes the possible number of apples aa and number of sweet potatoes ss Jenna purchases with \10.typeyouranswer...10. type your answer... a+typeyouranswer... type your answer... s=typeyouranswer...b)Writeanequationinslope−interceptformthatdescribesthepossiblenumberofapples type your answer... b) Write an equation in slope-intercept form that describes the possible number of apples aandnumberofsweetpotatoes and number of sweet potatoes sJennapurchaseswith$10. Jenna purchases with \$10. s= \squaretypeyouranswer... type your answer... a+typeyouranswer... type your answer... \squarec)IfJennaspends$10andpurchasesonly4apples,howmanysweetpotatoesdidshepurchase? c) If Jenna spends \$10 and purchases only 4 apples, how many sweet potatoes did she purchase? s=typeyouranswer...d)Usethecombinationofapplesandsweetpotatoesfrompart(c)towriteanequationinpoint−slopeformthatdescribesthepossiblenumberofapples type your answer... d) Use the combination of apples and sweet potatoes from part (c) to write an equation in point-slope form that describes the possible number of apples aandnumberofsweetpotatoes and number of sweet potatoes sJennapurchaseswith$10. Jenna purchases with \$10. s-typeyouranswer...=typeyouranswer... type your answer... = type your answer... \square(a−typeyouranswer...e)TrueorFalse:Thegraphbelowrepresentstherelationbetweenthepossiblenumberofapples (a- type your answer... e) True or False: The graph below represents the relation between the possible number of apples aandnumberofsweetpotatoes and number of sweet potatoes s$ Jenna purchases with \$10.

Studdy Solution

STEP 1

1. Jenna spends a total of 10onapplesandsweetpotatoes.<br/>2.Applescost10 on apples and sweet potatoes.<br />2. Apples cost 1.25 each.
3. Sweet potatoes cost $1 each.
4. Let \( a \) represent the number of apples purchased.
5. Let \( s \) represent the number of sweet potatoes purchased.

STEP 2

1. Write the equation in standard form.
2. Convert the equation to slope-intercept form.
3. Solve for the number of sweet potatoes when 4 apples are purchased.
4. Write the equation in point-slope form using the solution from part (c).
5. Evaluate the truth of the statement regarding the graph.

STEP 3

Write the equation in standard form.
The total cost of apples and sweet potatoes is $10. Therefore, the equation is:
1.25a+1s=10 1.25a + 1s = 10

STEP 4

Convert the equation to slope-intercept form.
Start with the standard form equation:
1.25a+s=10 1.25a + s = 10
Solve for s s :
s=−1.25a+10 s = -1.25a + 10

STEP 5

Solve for the number of sweet potatoes when 4 apples are purchased.
Substitute a=4 a = 4 into the equation:
s=−1.25(4)+10 s = -1.25(4) + 10
Calculate:
s=−5+10 s = -5 + 10 s=5 s = 5
Jenna purchased 5 sweet potatoes.

STEP 6

Write the equation in point-slope form using the solution from part (c).
Using the point (4, 5) and the slope from the slope-intercept form equation, −1.25-1.25:
s−5=−1.25(a−4) s - 5 = -1.25(a - 4)

STEP 7

Evaluate the truth of the statement regarding the graph.
To determine if the graph represents the relation, check if the line passes through the point (4, 5) and has a slope of −1.25-1.25. If both conditions are met, the statement is true; otherwise, it is false.

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